//chapter3 section 1 group 1 function_definition_notation //

 var tf_function_definition_notation_max_count = 12;
 
var tf_function_definition_notation_1 = 'Every function is an equation.';
var answer_tf_function_definition_notation_1 = 'false';
var feedback_right_tf_function_definition_notation_1 = 'CORRECT:  ';
var feedback_wrong_tf_function_definition_notation_1 = 'INCORRECT:   ';
 
 
var tf_function_definition_notation_2 = 'A function consists of a domain, a range, and a rule.';
var answer_tf_function_definition_notation_2 = 'true';
var feedback_right_tf_function_definition_notation_2 = 'CORRECT:  ';
var feedback_wrong_tf_function_definition_notation_2 = 'INCORRECT:  ';

var tf_function_definition_notation_3 = 'The domain of a function is a set of numbers.';
var answer_tf_function_definition_notation_3 = 'false';
var feedback_right_tf_function_definition_notation_3 = 'CORRECT:  ';
var feedback_wrong_tf_function_definition_notation_3 = 'INCORRECT:   ';
 

 var tf_function_definition_notation_4 = 'The range of a function is a set of rational numbers';
 var answer_tf_function_definition_notation_4 = 'false';
 var feedback_right_tf_function_definition_notation_4 = 'CORRECT:  ';
 var feedback_wrong_tf_function_definition_notation_4 = 'INCORRECT:  ';
 
 var tf_function_definition_notation_5 = 'The rule for a function must be an equation.';
 var answer_tf_function_definition_notation_5 = 'false';
 var feedback_right_tf_function_definition_notation_5 = 'CORRECT:  ';
 var feedback_wrong_tf_function_definition_notation_5 = 'INCORRECT:  '; 
 
 
 var tf_function_definition_notation_6 = 'In the expression f(x)the symbol x represents a domain.';
 var answer_tf_function_definition_notation_6 = 'false';
 var feedback_right_tf_function_definition_notation_6 = 'CORRECT:  ';
 var feedback_wrong_tf_function_definition_notation_6 = 'INCORRECT:  '; 
  
 var tf_function_definition_notation_7 = 'In the expression f(x)the symbol f represents the name of the function.';
 var answer_tf_function_definition_notation_7 = 'true';
 var feedback_right_tf_function_definition_notation_7 = 'CORRECT: ';
 var feedback_wrong_tf_function_definition_notation_7 = 'INCORRECT:  '; 

 
 var tf_function_definition_notation_8 = 'In the expression f(x)the symbol f(x) represents the range.';
 var answer_tf_function_definition_notation_8 = 'false';
 var feedback_right_tf_function_definition_notation_8 = 'CORRECT: ';
 var feedback_wrong_tf_function_definition_notation_8 = 'INCORRECT:  ';   
  
var tf_function_definition_notation_9 = 'If the rule of a function is presented as arrows, then an arrow must eminate from each range element.';
 var answer_tf_function_definition_notation_9 = 'false';
 var feedback_right_tf_function_definition_notation_9 = 'CORRECT: ';
 var feedback_wrong_tf_function_definition_notation_9 = 'INCORRECT:  ';
 
var tf_function_definition_notation_10 = 'If the rule of a function is presented as arrows, then an arrow must eminate from each domain element.';
 var answer_tf_function_definition_notation_10 = 'true';
 var feedback_right_tf_function_definition_notation_10 = 'CORRECT: ';
 var feedback_wrong_tf_function_definition_notation_10 = 'INCORRECT:  '; 
 
var tf_function_definition_notation_11 = 'If the rule of a function is presented as arrows, then an arrow must terminate at each range element.';
 var answer_tf_function_definition_notation_11 = 'false';
 var feedback_right_tf_function_definition_notation_11 = 'CORRECT: ';
 var feedback_wrong_tf_function_definition_notation_11 = 'INCORRECT:  ';  
 
var tf_function_definition_notation_12 = 'If the rule of a function is presented as arrows, then two arrows may terminate at a range element.';
 var answer_tf_function_definition_notation_12 = 'true';
 var feedback_right_tf_function_definition_notation_12 = 'CORRECT: ';
 var feedback_wrong_tf_function_definition_notation_12 = 'INCORRECT:  ';   

  //chapter3 section2 group1 function_graph //

 var tf_function_graph_max_count = 6;
 
var tf_function_graph_1 = 'Coordinates of points on the graph of a function f satisfy the rule of the function.';
var answer_tf_function_graph_1 = 'true';
var feedback_right_tf_function_graph_1 = 'CORRECT:  ';
var feedback_wrong_tf_function_graph_1 = 'INCORRECT:   '; 

var tf_function_graph_2 = 'If a vertical line may be drawn which intersects a graph in more than one point, then that graph is not the graph of a function.';
var answer_tf_function_graph_2 = 'true';
var feedback_right_tf_function_graph_2 = 'CORRECT:  ';
var feedback_wrong_tf_function_graph_2 = 'INCORRECT:   '; 

var tf_function_graph_3 = 'Zeros of a function are in the range of the function.';
var answer_tf_function_graph_3 = 'false';
var feedback_right_tf_function_graph_3 = 'CORRECT:  ';
var feedback_wrong_tf_function_graph_3 = 'INCORRECT:   '; 

var tf_function_graph_4 = 'A zero of a function is a domain element k for which f(k) = 0.';
var answer_tf_function_graph_4 = 'true';
var feedback_right_tf_function_graph_4 = 'CORRECT:  ';
var feedback_wrong_tf_function_graph_4 = 'INCORRECT:   '; 

var tf_function_graph_5 = 'The graph of a function consists of all those points of the form (a,f(a)) where a is a domain element and f(a) is the corresponding range element.';
var answer_tf_function_graph_5 = 'true';
var feedback_right_tf_function_graph_5 = 'CORRECT:  ';
var feedback_wrong_tf_function_graph_5 = 'INCORRECT:   '; 


var tf_function_graph_6 = 'Zeros of a function are in the domain of the function.';
var answer_tf_function_graph_6 = 'true';
var feedback_right_tf_function_graph_6 = 'CORRECT:  ';
var feedback_wrong_tf_function_graph_6 = 'INCORRECT:   '; 
 







  //chapter3 section 5 group 1 function_quadratic //

 var tf_function_quadratic_max_count = 16;
 
var tf_function_quadratic_1 = 'Every function is a quadratic equation.';
var answer_tf_function_quadratic_1 = 'false';
var feedback_right_tf_function_quadratic_1 = 'CORRECT:  ';
var feedback_wrong_tf_function_quadratic_1 = 'INCORRECT:   ';  
   
var tf_function_quadratic_2 = 'Every quadratic function is a function.';
var answer_tf_function_quadratic_2 = 'true';
var feedback_right_tf_function_quadratic_2 = 'CORRECT:  ';
var feedback_wrong_tf_function_quadratic_2 = 'INCORRECT:   '; 
   
var tf_function_quadratic_3 = 'Every quadratic function is a polynomial function.';
var answer_tf_function_quadratic_3 = 'true';
var feedback_right_tf_function_quadratic_3 = 'CORRECT:  ';
var feedback_wrong_tf_function_quadratic_3 = 'INCORRECT:   '; 
   
var tf_function_quadratic_4 = 'Linear functions are quadratic functions.';
var answer_tf_function_quadratic_4 = 'false';
var feedback_right_tf_function_quadratic_4 = 'CORRECT:  ';
var feedback_wrong_tf_function_quadratic_4 = 'INCORRECT:   ';    
  
var tf_function_quadratic_5 = 'A quadrtic function is a function whose rule may be written as ax<sup>2</sup> + bx + c = 0.';
var answer_tf_function_quadratic_5 = 'false';
var feedback_right_tf_function_quadratic_5 = 'CORRECT:  ';
var feedback_wrong_tf_function_quadratic_5 = 'INCORRECT:   '; 

var tf_function_quadratic_6 = 'A quadrtic function is a function whose rule may be written as f(x) = ax<sup>2</sup> + bx + c .';
var answer_tf_function_quadratic_6 = 'true';
var feedback_right_tf_function_quadratic_6 = 'CORRECT:  ';
var feedback_wrong_tf_function_quadratic_6 = 'INCORRECT:   '; 

var tf_function_quadratic_7 = 'f(x) = 3x -7 is the rule for a quadratic function.';
var answer_tf_function_quadratic_7 = 'false';
var feedback_right_tf_function_quadratic_7 = 'CORRECT:  ';
var feedback_wrong_tf_function_quadratic_7 = 'INCORRECT:   '; 

var tf_function_quadratic_8 = 'f(x) = 3x<sup>2</sup> - 5x + 9 is the rule for a quadratic function.';
var answer_tf_function_quadratic_8 = 'true';
var feedback_right_tf_function_quadratic_8 = 'CORRECT:  ';
var feedback_wrong_tf_function_quadratic_8 = 'INCORRECT:   '; 

var tf_function_quadratic_9 = 'The graph of quadratic function is a parabola.';
var answer_tf_function_quadratic_9 = 'true';
var feedback_right_tf_function_quadratic_9 = 'CORRECT:  ';
var feedback_wrong_tf_function_quadratic_9 = 'INCORRECT:   '; 

var tf_function_quadratic_10 = 'The graph of f(x) = x<sup>2</sup> - 5x + 6 crosses the x-axis two times.';
var answer_tf_function_quadratic_10 = 'true';
var feedback_right_tf_function_quadratic_10 = 'CORRECT:  ';
var feedback_wrong_tf_function_quadratic_10 = 'INCORRECT:   '; 

var tf_function_quadratic_11 = 'If the leading coefficient of a quadraqtic function is negative, the graph of the function opens up.';
var answer_tf_function_quadratic_11 = 'false';
var feedback_right_tf_function_quadratic_11 = 'CORRECT:  ';
var feedback_wrong_tf_function_quadratic_11 = 'INCORRECT:   '; 

var tf_function_quadratic_12 = 'If the leading coefficient of a quadraqtic function is positive, the graph of the function opens up.';
var answer_tf_function_quadratic_12 = 'true';
var feedback_right_tf_function_quadratic_12 = 'CORRECT:  ';
var feedback_wrong_tf_function_quadratic_12 = 'INCORRECT:   '; 

var tf_function_quadratic_13 = 'The graph of a quadratic function will cross the x-axis two times.';
var answer_tf_function_quadratic_13 = 'false';
var feedback_right_tf_function_quadratic_13 = 'CORRECT:  ';
var feedback_wrong_tf_function_quadratic_13 = 'INCORRECT:   '; 

var tf_function_quadratic_14 = 'The graph of some quadratic functions do not cross the x-axis.';
var answer_tf_function_quadratic_14 = 'true';
var feedback_right_tf_function_quadratic_14 = 'CORRECT:  ';
var feedback_wrong_tf_function_quadratic_14 = 'INCORRECT:   '; 

var tf_function_quadratic_15 = 'The first coordinate of the vertex of the graph of a quadratic function whose rule is f(x) =ax<sup>2</sup> + bx + c  is -b/2a.';
var answer_tf_function_quadratic_15 = 'true';
var feedback_right_tf_function_quadratic_15 = 'CORRECT:  ';
var feedback_wrong_tf_function_quadratic_15 = 'INCORRECT:   '; 

var tf_function_quadratic_16 = 'The second coordinate of the vertex of the graph of a quadratic function whose rule is f(x) =ax<sup>2</sup> + bx + c  is f(-b/2a).';
var answer_tf_function_quadratic_16 = 'true';
var feedback_right_tf_function_quadratic_16 = 'CORRECT:  ';
var feedback_wrong_tf_function_quadratic_16 = 'INCORRECT:   '; 


  //chapter3 section 6 group 1 function_combining //

 var tf_function_combining_max_count = 11;
 
var tf_function_combining_1 = 'The sum of two functions is a function.';
var answer_tf_function_combining_1 = 'true';
var feedback_right_tf_function_combining_1 = 'CORRECT:  ';
var feedback_wrong_tf_function_combining_1 = 'INCORRECT:   ';  

var tf_function_combining_2 = 'If f(3) = 2 and g(3) = 9, then f+g(2) = 11.';
var answer_tf_function_combining_2 = 'true';
var feedback_right_tf_function_combining_2 = 'CORRECT:  ';
var feedback_wrong_tf_function_combining_2 = 'INCORRECT:   '; 

var tf_function_combining_3 = 'If f and g are functions, then f+g is a function whose rule is f+g(x) = f(x) + g(x).';
var answer_tf_function_combining_3 = 'true';
var feedback_right_tf_function_combining_3 = 'CORRECT:  ';
var feedback_wrong_tf_function_combining_3 = 'INCORRECT:   ';  

var tf_function_combining_4 = 'The product of two functions is a number.';
var answer_tf_function_combining_4 = 'false';
var feedback_right_tf_function_combining_4 = 'CORRECT:  ';
var feedback_wrong_tf_function_combining_4 = 'INCORRECT:   ';  

var tf_function_combining_5 = 'If f and g are functions, then fg is a function whose rule is fg(x) = f(x) + g(x).';
var answer_tf_function_combining_5 = 'false';
var feedback_right_tf_function_combining_5 = 'CORRECT:  ';
var feedback_wrong_tf_function_combining_5 = 'INCORRECT:   ';  

var tf_function_combining_6 = 'The composition of two functions is a function.';
var answer_tf_function_combining_6 = 'true';
var feedback_right_tf_function_combining_6 = 'CORRECT:  ';
var feedback_wrong_tf_function_combining_6 = 'INCORRECT:   '; 

var tf_function_combining_7 = 'Composition is commutative.';
var answer_tf_function_combining_7 = 'false';
var feedback_right_tf_function_combining_7 = 'CORRECT:  ';
var feedback_wrong_tf_function_combining_7 = 'INCORRECT:   '; 

var tf_function_combining_8 = 'If f and g then the rule for the composition of f with g is given by f(g(x)) .';
var answer_tf_function_combining_8 = 'false';
var feedback_right_tf_function_combining_8 = 'CORRECT:  ';
var feedback_wrong_tf_function_combining_8 = 'INCORRECT:   '; 

var tf_function_combining_9 = 'If f(2)= 7 and g(5) = 2 and g(7) = 5, then f circle g of 5 is 7.';
var answer_tf_function_combining_9 = 'true';
var feedback_right_tf_function_combining_9 = 'CORRECT:  ';
var feedback_wrong_tf_function_combining_9 = 'INCORRECT:   '; 

var tf_function_combining_10 = 'If f(2)= 7 and g(5) = 2, then g circle f of 5 is 2.';
var answer_tf_function_combining_10 = 'false';
var feedback_right_tf_function_combining_10 = 'CORRECT:  ';
var feedback_wrong_tf_function_combining_10 = 'INCORRECT:   '; 

var tf_function_combining_11 = 'Composition is not commutative.';
var answer_tf_function_combining_11 = 'true';
var feedback_right_tf_function_combining_11 = 'CORRECT:  ';
var feedback_wrong_tf_function_combining_11 = 'INCORRECT:   '; 


  //chapter3 section 7 group 1 function_inverse //

 var tf_function_inverse_max_count = 10;
 
var tf_function_inverse_1 = 'Every function has an inverse.';
var answer_tf_function_inverse_1 = 'false';
var feedback_right_tf_function_inverse_1 = 'CORRECT:  ';
var feedback_wrong_tf_function_inverse_1 = 'INCORRECT:   ';  

var tf_function_inverse_2 = 'If f and g are functions and are inverses of each other, then f(g(x)) = x and g(f(x)) = x.';
var answer_tf_function_inverse_2 = 'true';
var feedback_right_tf_function_inverse_2 = 'CORRECT:  ';
var feedback_wrong_tf_function_inverse_2 = 'INCORRECT:   '; 

var tf_function_inverse_3 = 'If the graph of a function fails the horizontal line test, the function has no inverse.';
var answer_tf_function_inverse_3 = 'true';
var feedback_right_tf_function_inverse_3 = 'CORRECT:  ';
var feedback_wrong_tf_function_inverse_3 = 'INCORRECT:   '; 

var tf_function_inverse_4 = 'The symbol f<sup>-1</sup> is read as f inverse.';
var answer_tf_function_inverse_4 = 'true';
var feedback_right_tf_function_inverse_4 = 'CORRECT:  ';
var feedback_wrong_tf_function_inverse_4 = 'INCORRECT:   '; 

var tf_function_inverse_5 = 'Not all functions have inverses.';
var answer_tf_function_inverse_5 = 'true';
var feedback_right_tf_function_inverse_5 = 'CORRECT:  ';
var feedback_wrong_tf_function_inverse_5 = 'INCORRECT:   '; 

var tf_function_inverse_6 = 'The functions f and f<sup>-1</sup> are inverses of each other.';
var answer_tf_function_inverse_6 = 'true';
var feedback_right_tf_function_inverse_6 = 'CORRECT:  ';
var feedback_wrong_tf_function_inverse_6 = 'INCORRECT:   '; 

var tf_function_inverse_7 = 'If no horizontal line intersects the graph of a function f in more than one point, then the function f has an inverse.';
var answer_tf_function_inverse_7 = 'true';
var feedback_right_tf_function_inverse_7 = 'CORRECT:  ';
var feedback_wrong_tf_function_inverse_7 = 'INCORRECT:   '; 

var tf_function_inverse_8 = 'Every linear function has an inverse.';
var answer_tf_function_inverse_8 = 'false';
var feedback_right_tf_function_inverse_8 = 'CORRECT:  ';
var feedback_wrong_tf_function_inverse_8 = 'INCORRECT:   '; 

var tf_function_inverse_9 = 'Some quadratic functions have an inverse.';
var answer_tf_function_inverse_9 = 'false';
var feedback_right_tf_function_inverse_9 = 'CORRECT:  ';
var feedback_wrong_tf_function_inverse_9 = 'INCORRECT:   '; 

var tf_function_inverse_10 = 'Non-constant linear functions have inverses.';
var answer_tf_function_inverse_10 = 'true';
var feedback_right_tf_function_inverse_10 = 'CORRECT:  ';
var feedback_wrong_tf_function_inverse_10 = 'INCORRECT:   '; 


  //chapter4 section1 group1 function_polynomial_definition //

 var tf_function_polynomial_definition_max_count = 8;
 
var tf_function_polynomial_definition_1 = 'The degree of a polynomial function is the degree of the first term.';
var answer_tf_function_polynomial_definition_1 = 'false';
var feedback_right_tf_function_polynomial_definition_1 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_definition_1 = 'INCORRECT:   ';  

var tf_function_polynomial_definition_2 = 'The graph of a polynomial function has sharp corners.';
var answer_tf_function_polynomial_definition_2 = 'false';
var feedback_right_tf_function_polynomial_definition_2 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_definition_2 = 'INCORRECT:   ';  

var tf_function_polynomial_definition_3 = 'A linear function is a polynomial function.';
var answer_tf_function_polynomial_definition_3 = 'true';
var feedback_right_tf_function_polynomial_definition_3 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_definition_3 = 'INCORRECT:   ';  

var tf_function_polynomial_definition_3 = 'A polynomial function is a quadratic function.';
var answer_tf_function_polynomial_definition_3 = 'false';
var feedback_right_tf_function_polynomial_definition_3 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_definition_3 = 'INCORRECT:   ';  

var tf_function_polynomial_definition_4 = 'A quadratic function function is a polynomial function.';
var answer_tf_function_polynomial_definition_4 = 'true';
var feedback_right_tf_function_polynomial_definition_4 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_definition_4 = 'INCORRECT:   ';  

var tf_function_polynomial_definition_5 = 'The degree of a polynomial function is the degree of the leading term.';
var answer_tf_function_polynomial_definition_5 = 'true';
var feedback_right_tf_function_polynomial_definition_5 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_definition_5 = 'INCORRECT:   ';  

var tf_function_polynomial_definition_6 = 'The graph of a polynomial is a smooth continuous curve with no sharp corners.';
var answer_tf_function_polynomial_definition_6 = 'true';
var feedback_right_tf_function_polynomial_definition_6 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_definition_6 = 'INCORRECT:   ';  

var tf_function_polynomial_definition_7 = 'The graph of a third degree polynomial function tries to cross the x-axis three times.';
var answer_tf_function_polynomial_definition_7 = 'true';
var feedback_right_tf_function_polynomial_definition_7 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_definition_7 = 'INCORRECT:   ';  

var tf_function_polynomial_definition_8 = 'The graph of a polynomial function may have holes in it.';
var answer_tf_function_polynomial_definition_8 = 'false';
var feedback_right_tf_function_polynomial_definition_8 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_definition_8 = 'INCORRECT:   '; 

  //chapter4 section1 group2 function_polynomial_equivalent_statements //

 var tf_function_polynomial_equivalent_statements_max_count = 2;
 
var tf_function_polynomial_equivalent_statements_1 = 'If f is a polynomial function, k is a real number,  and f(k) = 0, then (k, 0) is an x-intercept of the graph of the funtion f.';
var answer_tf_function_polynomial_equivalent_statements_1 = 'true';
var feedback_right_tf_function_polynomial_equivalent_statements_1 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_equivalent_statements_1 = 'INCORRECT:   '; 

var tf_function_polynomial_equivalent_statements_2 = 'If k is a real number and x - k is a factor of a<sub>n</sub>x<sup>n</sup> + a<sub>n-1</sub>x<sup>n-1</sup> + ... + a<sub>1</sub>x + a<sub>0</sub>, then k is a real zero of the polynomial function whose rule is f(x) = a<sub>n</sub>x<sup>n</sup> + a<sub>n-1</sub>x<sup>n-1</sup> + ... + a<sub>1</sub>x + a<sub>0</sub>.';
var answer_tf_function_polynomial_equivalent_statements_2 = 'true';
var feedback_right_tf_function_polynomial_equivalent_statements_2 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_equivalent_statements_2 = 'INCORRECT:   '; 

 var tf_function_polynomial_multiplicities_max_count = 4;
 
var tf_function_polynomial_multiplicities_1 = 'If the multiplicity of a real zero of a polynomial function is an even number, then that zero is not an x-intercept.';
var answer_tf_function_polynomial_multiplicities_1 = 'false';
var feedback_right_tf_function_polynomial_multiplicities_1 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_multiplicities_1 = 'INCORRECT:   '; 

var tf_function_polynomial_multiplicities_2 = 'If f(x) = (x - 3)<sup>7</sup>, then 3 is a zero of multiplicity 7.';
var answer_tf_function_polynomial_multiplicities_2 = 'true';
var feedback_right_tf_function_polynomial_multiplicities_2 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_multiplicities_2 = 'INCORRECT:   '; 

var tf_function_polynomial_multiplicities_3 = 'If k is a real zero of a polynomial function f and if the multiplicity of the zero k is odd then the graph of f will cross the x-axis.';
var answer_tf_function_polynomial_multiplicities_3 = 'true';
var feedback_right_tf_function_polynomial_multiplicities_3 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_multiplicities_3 = 'INCORRECT:   '; 

var tf_function_polynomial_multiplicities_4 = 'If k is a real zero of a polynomial function f and if the multiplicity of the zero k is even then the graph of f will cross the x-axis.';
var answer_tf_function_polynomial_multiplicities_4 = 'false';
var feedback_right_tf_function_polynomial_multiplicities_4 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_multiplicities_4 = 'INCORRECT:   '; 

 var tf_function_polynomial_intermediate_value_max_count = 2;
 
var tf_function_polynomial_intermediate_value_1 = 'If f is a polynomial function for which f(3) < 0 and f(4) > 0, then f has a real zero in the interval (3, 4).';
var answer_tf_function_polynomial_intermediate_value_1 = 'true';
var feedback_right_tf_function_polynomial_intermediate_value_1 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_intermediate_value_1 = 'INCORRECT:   '; 

var tf_function_polynomial_intermediate_value_2 = 'If f is a polynomial function for which f(3) < 0 and f(4) > 0, then f may have multiple real zeros in the interval (3, 4).';
var answer_tf_function_polynomial_intermediate_value_2 = 'true';
var feedback_right_tf_function_polynomial_intermediate_value_2 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_intermediate_value_2 = 'INCORRECT:   '; 

 var tf_function_polynomial_dividing_max_count = 4;
 
var tf_function_polynomial_dividing_1 = 'If a and b are natural numbers then there are unique natural numbers q and r such that a = bq + r with 0&le; < r < b.';
var answer_tf_function_polynomial_dividing_1 = 'true';
var feedback_right_tf_function_polynomial_dividing_1 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_dividing_1 = 'INCORRECT:   '; 

var tf_function_polynomial_dividing_2 = 'Long division is a process for calculating the quotient and remainder whose existence is assured by the Division Algorithm.';
var answer_tf_function_polynomial_dividing_2 = 'true';
var feedback_right_tf_function_polynomial_dividing_2 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_dividing_2 = 'INCORRECT:   '; 

var tf_function_polynomial_dividing_3 = 'If a fifth degree polynomial is divided by a third degree polynomial, the quotient will have degree four.';
var answer_tf_function_polynomial_dividing_3 = 'false';
var feedback_right_tf_function_polynomial_dividing_3 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_dividing_3 = 'INCORRECT:   '; 

var tf_function_polynomial_dividing_4 = 'If p, q, and d are polynomials such that p = qd then we say p is divisible by q.';
var answer_tf_function_polynomial_dividing_4 = 'true';
var feedback_right_tf_function_polynomial_dividing_4 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_dividing_4 = 'INCORRECT:   '; 

 var tf_function_polynomial_remainder_factor_max_count = 2;
 
var tf_function_polynomial_remainder_factor_1 = 'If a polynomial function f is divided by the polynomial function g whose rule is g(x) = x - k, the remainder will be f(k).';
var answer_tf_function_polynomial_remainder_factor_1 = 'true';
var feedback_right_tf_function_polynomial_remainder_factor_1 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_remainder_factor_1 = 'INCORRECT:   '; 

var tf_function_polynomial_remainder_factor_2 = 'If k is a zero of the polynomial function f, then f is divisible by the linear function whose rule is g(x) = x - k.';
var answer_tf_function_polynomial_remainder_factor_2 = 'true';
var feedback_right_tf_function_polynomial_remainder_factor_2 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_remainder_factor_2 = 'INCORRECT:   '; 

 var tf_function_polynomial_real_zeros_max_count = 6;
 
var tf_function_polynomial_real_zeros_1 = 'If p/q is a rational zero of the polynomial function f(x) = 4x<sup>5</sup> + 3x<sup>4</sup> + ... + 11x + 3, then p is a divisor of 4.';
var answer_tf_function_polynomial_real_zeros_1 = 'false';
var feedback_right_tf_function_polynomial_real_zeros_1 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_real_zeros_1 = 'INCORRECT:   '; 

var tf_function_polynomial_real_zeros_2 = 'If p/q is a rational zero of the polynomial function f(x) = 4x<sup>5</sup> + 3x<sup>4</sup> + ... + 11x + 3, then q is a divisor of 4.';
var answer_tf_function_polynomial_real_zeros_2 = 'true';
var feedback_right_tf_function_polynomial_real_zeros_2 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_real_zeros_2 = 'INCORRECT:   '; 

var tf_function_polynomial_real_zeros_3 = 'If p/q is a rational zero of the polynomial function f(x) = 4x<sup>5</sup> + 3x<sup>4</sup> + ... + 11x + 3, then p is a divisor of 3.';
var answer_tf_function_polynomial_real_zeros_3 = 'true';
var feedback_right_tf_function_polynomial_real_zeros_3 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_real_zeros_3 = 'INCORRECT:   '; 

var tf_function_polynomial_real_zeros_4 = 'If p/q is a rational zero of the polynomial function f(x) = 4x<sup>5</sup> + 3x<sup>4</sup> + ... + 11x + 3, then q is a divisor of 3.';
var answer_tf_function_polynomial_real_zeros_4 = 'false';
var feedback_right_tf_function_polynomial_real_zeros_4 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_real_zeros_4 = 'INCORRECT:   ';

var tf_function_polynomial_real_zeros_5 = 'If the leading coefficient of a polynomial function is 1, then the possible rational zeros are integers.';
var answer_tf_function_polynomial_real_zeros_5 = 'true';
var feedback_right_tf_function_polynomial_real_zeros_5 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_real_zeros_5 = 'INCORRECT:   ';

var tf_function_polynomial_real_zeros_6 = 'If the leading coefficient of a polynomial function is 1, then the possible rational zeros are natural numbers.';
var answer_tf_function_polynomial_real_zeros_6 = 'false';
var feedback_right_tf_function_polynomial_real_zeros_6 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_real_zeros_6 = 'INCORRECT:   ';

 var tf_function_polynomial_complex_zeros_max_count = 7;
 
var tf_function_polynomial_complex_zeros_1 = 'If f is a polynomial function of degree n, then f has exactly n complex zeros.';
var answer_tf_function_polynomial_complex_zeros_1 = 'true';
var feedback_right_tf_function_polynomial_complex_zeros_1 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_complex_zeros_1 = 'INCORRECT:   '; 

var tf_function_polynomial_complex_zeros_2 = 'If a + bi is a complex zero of the polynomial function f, then -a - bi is also a zero of f.';
var answer_tf_function_polynomial_complex_zeros_2 = 'false';
var feedback_right_tf_function_polynomial_complex_zeros_2 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_complex_zeros_2 = 'INCORRECT:   '; 

var tf_function_polynomial_complex_zeros_3 = 'Complex zeros of polynomial functions occur in conjugate pairs.';
var answer_tf_function_polynomial_complex_zeros_3 = 'true';
var feedback_right_tf_function_polynomial_complex_zeros_2 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_complex_zeros_2 = 'INCORRECT:   '; 

var tf_function_polynomial_complex_zeros_4 = 'A third degree polynomial must cross the x-axis at least once.';
var answer_tf_function_polynomial_complex_zeros_4 = 'true';
var feedback_right_tf_function_polynomial_complex_zeros_4 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_complex_zeros_4 = 'INCORRECT:   '; 

var tf_function_polynomial_complex_zeros_5 = 'A sixth degree polynomial must cross the x-axis at least once.';
var answer_tf_function_polynomial_complex_zeros_5 = 'false';
var feedback_right_tf_function_polynomial_complex_zeros_5 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_complex_zeros_5 = 'INCORRECT:   '; 

var tf_function_polynomial_complex_zeros_6 = 'Every polynomial with positive degree can be written as the product of linear factors with real coefficients.';
var answer_tf_function_polynomial_complex_zeros_6 = 'false';
var feedback_right_tf_function_polynomial_complex_zeros_6 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_complex_zeros_6 = 'INCORRECT:   '; 

var tf_function_polynomial_complex_zeros_7 = 'Every polynomial with positive degree can be written as the product of linear and quadratic factors with real coefficients.';
var answer_tf_function_polynomial_complex_zeros_7 = 'true';
var feedback_right_tf_function_polynomial_complex_zeros_7 = 'CORRECT:  ';
var feedback_wrong_tf_function_polynomial_complex_zeros_7 = 'INCORRECT:   '; 

 var tf_function_rational_definition_max_count = 9;
 
var tf_function_rational_definition_1 = 'If the rule for a function contains rational numbers, then that function is called a rational function.';
var answer_tf_function_rational_definition_1 = 'false';
var feedback_right_tf_function_rational_definition_1 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_definition_1 = 'INCORRECT:   '; 

var tf_function_rational_definition_2 = 'If the rule for a polynomial function contains rational exponents, the function is called a rational function.';
var answer_tf_function_rational_definition_2 = 'false';
var feedback_right_tf_function_rational_definition_2 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_definition_2 = 'INCORRECT:   '; 

var tf_function_rational_definition_3 = 'The rule for a rational function can be written as the quotient of two polynomial functions.';
var answer_tf_function_rational_definition_3 = 'true';
var feedback_right_tf_function_rational_definition_3 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_definition_3 = 'INCORRECT:   '; 

var tf_function_rational_definition_4 = 'The domain of a rational function is all real numbers except the zeros of the numerator and zeros of the denominator.';
var answer_tf_function_rational_definition_4 = 'false';
var feedback_right_tf_function_rational_definition_4 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_definition_4 = 'INCORRECT:   ';

var tf_function_rational_definition_5 = 'The domain of a rational function is all real numbers except the zeros of the numerator.';
var answer_tf_function_rational_definition_5 = 'false';
var feedback_right_tf_function_rational_definition_5 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_definition_5 = 'INCORRECT:   ';

var tf_function_rational_definition_6 = 'The domain of a rational function is all real numbers except the zeros of the denominator.';
var answer_tf_function_rational_definition_6 = 'true';
var feedback_right_tf_function_rational_definition_6 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_definition_6 = 'INCORRECT:   ';

var tf_function_rational_definition_7 = 'The zeros of a rational function is all real numbers except the zeros of the numerator and zeros of the denominator.';
var answer_tf_function_rational_definition_7 = 'false';
var feedback_right_tf_function_rational_definition_7 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_definition_7 = 'INCORRECT:   ';

var tf_function_rational_definition_8 = 'The zeros of a rational function is all real numbers except the zeros of the numerator.';
var answer_tf_function_rational_definition_8 = 'false';
var feedback_right_tf_function_rational_definition_8 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_definition_8 = 'INCORRECT:   ';

var tf_function_rational_definition_9 = 'The zeros of a rational function is all real numbers except the zeros of the denominator.';
var answer_tf_function_rational_definition_9 = 'true';
var feedback_right_tf_function_rational_definition_9 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_definition_9 = 'INCORRECT:   ';

 var tf_function_rational_vertical_asymptotes_max_count = 4;
 
var tf_function_rational_vertical_asymptotes_1 = 'Vertical asymptotes of a rational function occur at real zeros of the numerator which are not zeros of the denominator.';
var answer_tf_function_rational_vertical_asymptotes_1 = 'false';
var feedback_right_tf_function_rational_vertical_asymptotes_1 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_vertical_asymptotes_1 = 'INCORRECT:   '; 

var tf_function_rational_vertical_asymptotes_2 = 'Vertical asymptotes of a rational function occur at real zeros of the denominator which are not zeros of the numerator.';
var answer_tf_function_rational_vertical_asymptotes_2 = 'true';
var feedback_right_tf_function_rational_vertical_asymptotes_2 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_vertical_asymptotes_2 = 'INCORRECT:   '; 

var tf_function_rational_vertical_asymptotes_3 = 'To find the vertical asymptotes of a rational function find the real zeros of the denominator and eliminate those which are zeros of the numerator.';
var answer_tf_function_rational_vertical_asymptotes_3 = 'true';
var feedback_right_tf_function_rational_vertical_asymptotes_3 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_vertical_asymptotes_3 = 'INCORRECT:   '; 

var tf_function_rational_vertical_asymptotes_4 = 'Vertical asymptotes of a rational function occur at complex zeros of the denominator which are not zeros of the numerator.';
var answer_tf_function_rational_vertical_asymptotes_4 = 'false';
var feedback_right_tf_function_rational_vertical_asymptotes_4 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_vertical_asymptotes_4 = 'INCORRECT:   '; 

 var tf_function_rational_horizontal_asymptotes_max_count = 7;
 
var tf_function_rational_horizontal_asymptotes_1 = 'If f is a rational function and the degree of the numerator is less than the degree of the denominator, then y = 0 is a horizontal asymptote for f.';
var answer_tf_function_rational_horizontal_asymptotes_1 = 'true';
var feedback_right_tf_function_rational_horizontal_asymptotes_1 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_horizontal_asymptotes_1 = 'INCORRECT:   '; 

var tf_function_rational_horizontal_asymptotes_2 = 'If f is a rational function and the degree of the numerator is equal to the degree of the denominator, then f has no  horizontal asymptote for f.';
var answer_tf_function_rational_horizontal_asymptotes_2 = 'false';
var feedback_right_tf_function_rational_horizontal_asymptotes_2 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_horizontal_asymptotes_2 = 'INCORRECT:   '; 

var tf_function_rational_horizontal_asymptotes_3 = 'If f is a rational function and the degree of the numerator is equal to the degree of the denominator, then y = 0 is a horizontal asymptote for f.';
var answer_tf_function_rational_horizontal_asymptotes_3 = 'false';
var feedback_right_tf_function_rational_horizontal_asymptotes_3 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_horizontal_asymptotes_3 = 'INCORRECT:   '; 

var tf_function_rational_horizontal_asymptotes_4 = 'If f is a rational function and the degree of the numerator is greater than the degree of the denominator, then y = 0 is a horizontal asymptote for f.';
var answer_tf_function_rational_horizontal_asymptotes_4 = 'false';
var feedback_right_tf_function_rational_horizontal_asymptotes_4 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_horizontal_asymptotes_4 = 'INCORRECT:   '; 

var tf_function_rational_horizontal_asymptotes_5 = 'If f is a rational function and the degree of the numerator is greater than the degree of the denominator, then there is no horizontal asymptote for f.';
var answer_tf_function_rational_horizontal_asymptotes_5 = 'true';
var feedback_right_tf_function_rational_horizontal_asymptotes_5 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_horizontal_asymptotes_5 = 'INCORRECT:   '; 

var tf_function_rational_horizontal_asymptotes_6 = 'If f is a rational function and the degree of the numerator is greater than the degree of the denominator, then y = a/b (where a is the leading coefficient of the numerator and b is the leading coefficient of the denominator) is a horizontal asymptote for f.';
var answer_tf_function_rational_horizontal_asymptotes_6 = 'false';
var feedback_right_tf_function_rational_horizontal_asymptotes_6 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_horizontal_asymptotes_6 = 'INCORRECT:   '; 

var tf_function_rational_horizontal_asymptotes_7 = 'If f is a rational function and the degree of the numerator is equal to the degree of the denominator, then y = a/b (where a is the leading coefficient of the numerator and b is the leading coefficient of the denominator) is a horizontal asymptote for f.';
var answer_tf_function_rational_horizontal_asymptotes_7 = 'true';
var feedback_right_tf_function_rational_horizontal_asymptotes_7 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_horizontal_asymptotes_7 = 'INCORRECT:   '; 

 var tf_function_rational_important_facts_max_count = 11;
 
var tf_function_rational_important_facts_1 = 'The graph of a rational function may interesect its vertical asymptotes.';
var answer_tf_function_rational_important_facts_1 = 'false';
var feedback_right_tf_function_rational_important_facts_1 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_important_facts_1 = 'INCORRECT:   '; 

var tf_function_rational_important_facts_2 = 'The graph of a rational function may interesect its horizontal asymptote if it has one.';
var answer_tf_function_rational_important_facts_2 = 'true';
var feedback_right_tf_function_rational_important_facts_2 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_important_facts_2 = 'INCORRECT:   '; 

var tf_function_rational_important_facts_3 = 'The graph of a rational function may interesect its vertical asymptotes two or more times.';
var answer_tf_function_rational_important_facts_3 = 'false';
var feedback_right_tf_function_rational_important_facts_3 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_important_facts_3 = 'INCORRECT:   '; 

var tf_function_rational_important_facts_4 = 'The graph of a rational function may interesect its horizontal asymptote, if it has one, two or more times.';
var answer_tf_function_rational_important_facts_4 = 'true';
var feedback_right_tf_function_rational_important_facts_4 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_important_facts_4 = 'INCORRECT:   '; 

var tf_function_rational_important_facts_5 = 'If k is a zero of both numerator and denominator of a rational function f, then f has a vertical asymptote at x = k';
var answer_tf_function_rational_important_facts_5 = 'false';
var feedback_right_tf_function_rational_important_facts_5 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_important_facts_5 = 'INCORRECT:   '; 

var tf_function_rational_important_facts_6 = 'If k is a zero of both numerator and denominator of a rational function f, then f has a horizontal asymptote at y = k';
var answer_tf_function_rational_important_facts_6 = 'false';
var feedback_right_tf_function_rational_important_facts_6 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_important_facts_6 = 'INCORRECT:   '; 

var tf_function_rational_important_facts_7 = 'If k is a zero of both numerator and denominator of a rational function f, then f has a hole in the graph at x = k';
var answer_tf_function_rational_important_facts_7 = 'true';
var feedback_right_tf_function_rational_important_facts_7 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_important_facts_7 = 'INCORRECT:   '; 

var tf_function_rational_important_facts_8 = 'If f is a rational function, then f has at least one vertical asymptote.';
var answer_tf_function_rational_important_facts_8 = 'false';
var feedback_right_tf_function_rational_important_facts_8 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_important_facts_8 = 'INCORRECT:   '; 

var tf_function_rational_important_facts_9 = 'If f is a rational function, then f has at least one horizontal asymptote.';
var answer_tf_function_rational_important_facts_9 = 'false';
var feedback_right_tf_function_rational_important_facts_9 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_important_facts_9 = 'INCORRECT:   '; 

var tf_function_rational_important_facts_10 = 'If f is a rational function, then f may have more than one vertical asymptote.';
var answer_tf_function_rational_important_facts_10 = 'true';
var feedback_right_tf_function_rational_important_facts_10 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_important_facts_10 = 'INCORRECT:   '; 

var tf_function_rational_important_facts_11 = 'If f is a rational function, then f may have more than one horizontal asymptote.';
var answer_tf_function_rational_important_facts_11 = 'false';
var feedback_right_tf_function_rational_important_facts_11 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_important_facts_11 = 'INCORRECT:   '; 

var tf_function_rational_important_facts_11 = 'If f is a rational function with both a horizontal asymptote and vertical asymptotes, then the horizontal asymptote intersects each of the vertical asymptotes.';
var answer_tf_function_rational_important_facts_11 = 'true';
var feedback_right_tf_function_rational_important_facts_11 = 'CORRECT:  ';
var feedback_wrong_tf_function_rational_important_facts_11 = 'INCORRECT:   ';