//chapter3 section1 group1 function_definition_notation //

 var san_function_definition_notation_max_count = 5;
 
 var san_function_definition_notation_1 = 'The rule for a function is an equation';
 var answer_san_function_definition_notation_1 = 'sometimes';
  var feedback_right_san_function_definition_notation_1 = 'CORRECT: Can you provide an example of a function whose rule is not an equation ? ';
  var feedback_wrong_san_function_definition_notation_1 = 'INCORRECT: The rule for some functions is presented via a collection of arrows, the rules for other functions are more complex than an equation, and some rules are presented as equations. ';
 
 
var san_function_definition_notation_2 = 'The domain of a function is a set of numbers.';
 var answer_san_function_definition_notation_2 = 'sometimes';
  var feedback_right_san_function_definition_notation_2 = 'CORRECT: Can you provide an example of a function whose domain is not a set of numbers.';
  var feedback_wrong_san_function_definition_notation_2 = 'INCORRECT:  Nothing in the definition of a function requires that the domain be a set of numbers.'; 

 
var san_function_definition_notation_3 = 'The domain of a function is a set.';
 var answer_san_function_definition_notation_3 = 'always';
  var feedback_right_san_function_definition_notation_3 = 'CORRECT: ';
  var feedback_wrong_san_function_definition_notation_3 = 'INCORRECT:  Perhaps you should study the definition of function.'; 
 
 var san_function_definition_notation_4 = 'The symbol f(x) represents the unique range element associated with the domain element x by the function f.';
 var answer_san_function_definition_notation_4 = 'always';
  var feedback_right_san_function_definition_notation_4 = 'CORRECT:';
  var feedback_wrong_san_function_definition_notation_4 = 'INCORRECT:  A review and more complete study of function notation in the chapter summary is in order.';
 
 var san_function_definition_notation_5 = 'The rule for a function associates each element of the domain with a unique element of the range.';
 var answer_san_function_definition_notation_5 = 'always';
  var feedback_right_san_function_definition_notation_5 = 'CORRECT:  Can you provide examples of things that fail to be functions because they violate one part of this restriction on the rule for a function.';
  var feedback_wrong_san_function_definition_notation_5 = 'INCORRECT: Please review, study, memorize and learn the definition of function'; 
 


//chapter3 section2 group1 function_graph //

 var san_function_graph_max_count = 4;
 
var san_function_graph_1 = 'A zero of a function is a domain element.';
var answer_san_function_graph_1 = 'always';
var feedback_right_san_function_graph_1 = 'CORRECT:  ';
var feedback_wrong_san_function_graph_1 = 'INCORRECT:  The definition of zero of a function begins with the condition that a zero of a function be a domain element.';

var san_function_graph_2 = 'A vertical line may intersect the graph of a function in two points.';
var answer_san_function_graph_2 = 'never';
var feedback_right_san_function_graph_2 = 'CORRECT:  Did you rely on the definition of function or on the vertical line test?  What is the relation between these two ?';
var feedback_wrong_san_function_graph_2 = 'INCORRECT:  This would violate the "unique" requirement in the definition of function.  Please learn that definition.  It will also help you if you know and understand the vertical line test.';

var san_function_graph_3 = 'If k is a domain element then the point (k, f(k)) is on the graph of the function f.';
var answer_san_function_graph_3 = 'always';
var feedback_right_san_function_graph_3 = 'CORRECT:  ';
var feedback_wrong_san_function_graph_3 = 'INCORRECT:  Please learn the definiton of graph.';

var san_function_graph_4 = 'A zero of a function is a range element.';
var answer_san_function_graph_4 = 'never';
var feedback_right_san_function_graph_4 = 'CORRECT:  ';
var feedback_wrong_san_function_graph_4 = 'INCORRECT:  Absolutely not!  Look at the definiton of zero of a function.  Learn it!';


 //chapter3 section 5 group 1 function_quadratic //

 var san_function_quadratic_max_count = 11;
 
var san_function_quadratic_1 = 'A quadratic function is a function whose rule may be written in the form f(x) = ax<sup>2</sup> +bx + c.';
var answer_san_function_quadratic_1 = 'always';
var feedback_right_san_function_quadratic_1 = 'CORRECT:  ';
var feedback_wrong_san_function_quadratic_1 = 'INCORRECT:  Study the definition of quadratic function.';

var san_function_quadratic_2 = 'A quadratic function has no real zeros.';
var answer_san_function_quadratic_2 = 'sometimes';
var feedback_right_san_function_quadratic_2 = 'CORRECT:  Can you provide an example of a quadratic function which has no real zero?';
var feedback_wrong_san_function_quadratic_2 = 'INCORRECT: What about f(x) = x<sup>2</sup> + x + 1 ?.';

var san_function_quadratic_3 = 'The graph of a quadratic function has no x-intercepts.';
var answer_san_function_quadratic_3 = 'sometimes';
var feedback_right_san_function_quadratic_3 = 'CORRECT:  Can you provide an example of a parabola which opens up and has no x-intercept ? ';
var feedback_wrong_san_function_quadratic_3 = 'INCORRECT:  Can you draw a parabola which opens up and does not cross the x-axis ? Is it the graph of a quadratic function ? .'

var san_function_quadratic_4 = 'A quadratic function has two real zeros.';
var answer_san_function_quadratic_4 = 'sometimes';
var feedback_right_san_function_quadratic_4 = 'CORRECT: Can you provide an example?';
var feedback_wrong_san_function_quadratic_4 = 'INCORRECT: What about f(x) = (x + 1)(x - 5) ? .';

var san_function_quadratic_5 = 'The vertex of the graph of a quadratic function is on the x-intercept.';
var answer_san_function_quadratic_5 = 'sometimes';
var feedback_right_san_function_quadratic_5 = 'CORRECT:  ';
var feedback_wrong_san_function_quadratic_5 = 'INCORRECT:  The vertex of the graph of a quadratic function is the lowest (or highest) point on the graph.  This point can be on the x-axis but need not be on the x-axis.';

var san_function_quadratic_6 = 'A quadratic function has one real zero.';
var answer_san_function_quadratic_6 = 'sometimes';
var feedback_right_san_function_quadratic_6 = 'CORRECT:  Can you provide an example to illustrate each posibility ?';
var feedback_wrong_san_function_quadratic_6 = 'INCORRECT: What about f(x) = (x - 3)<sup>2</sup> ? .';

var san_function_quadratic_7 = 'The graph of a quadratic function has two x-intercepts.';
var answer_san_function_quadratic_7 = 'sometimes';
var feedback_right_san_function_quadratic_7 = 'CORRECT:  Can you provide an example ?';
var feedback_wrong_san_function_quadratic_7 = 'INCORRECT: Draw a parabola which opens up and crosses the x-axis twice.  Is it the graph of a quadratic function?';

var san_function_quadratic_8 = 'A quadratic function has more than two real zeros.';
var answer_san_function_quadratic_8 = 'never';
var feedback_right_san_function_quadratic_8 = 'CORRECT:  What was the basis for your choice?';
var feedback_wrong_san_function_quadratic_8 = 'INCORRECT:  Critically examine the quadratic formula.';

var san_function_quadratic_9 = 'The graph of a quadratic function opens up.';
var answer_san_function_quadratic_9 = 'sometimes';
var feedback_right_san_function_quadratic_9 = 'CORRECT:  ';
var feedback_wrong_san_function_quadratic_9 = 'INCORRECT:  If the leading coefficient is positive the parabola opens up, otherwise it opens down.';

var san_function_quadratic_10 = 'The graph of a quadratic function is a parabola.';
var answer_san_function_quadratic_10 = 'always';
var feedback_right_san_function_quadratic_10 = 'CORRECT: Take my word for it -- the graph of a quadratic function is always a parabola. ';
var feedback_wrong_san_function_quadratic_10 = 'INCORRECT:  Take my word for it -- the graph of a quadratic function is always a parabola.';

var san_function_quadratic_11 = 'The zeros of a quadratic function f are found by solving the equation resulting from f(x) = 0.';
var answer_san_function_quadratic_11 = 'always';
var feedback_right_san_function_quadratic_11 = 'CORRECT: This is a specific application of a general principle.  Can you state the general principle? ';
var feedback_wrong_san_function_quadratic_11 = 'INCORRECT:  The zeros of any function f are found by solving the equation resulting from f(x) = 0.   A quadratic function is no exception.';