MATH
140 -- Intermediate Algebra -- Exercise Solutions
Section: 3.2
44.
Is y = x - 1 a function.
Answer: Yes it can
be written as f(x) = x - 1 which matches the definition of a linear function.
45.
Is x = 2y2 a function.
Answer: NO Because
if x = 8, then y can be either 2 or -2. That is two elements (2 and -2) of
the range are associated with an element (8) of the domain. The same is true
for many other elemnts of the domain. For example, 18 is associated with both
3 and -3.
46.
Is y = x2 a function.
Answer: Yes it can
be written as f(x) = x2 which is the definition of aquadratic function.
48.
Is 2x - 3y = 9 a function.
Answer: Yes it is a
linear equation in standard form and can be rewritten in slope-intercept form
and then converted to f(x) =
x
- 3 which matches the definition of a linear function.
50.
Is 
a function.
Answer: Yes because
each value of x (other than 3) yields exactly one value of y. Furthermore
it matches the definiton of a rational function ( covered in a later section)
56.
If f is a function whose rule is f(x) = 3x + 3,
what is f(-1)?
Answer:
f(-1) is the unique range element associated with the domain element -1 by
the function f.
Using the rule for calculating the range element associated with -1 we obtain
f(-1) = 3(-1) + 3 = 0.
f(-1) = 0
58.
If h is a function whose rule is h(x) = 5x2
- 7, what is h(0)?
Answer:
h(0) is the unique range element associated with the domain element 0 by the
function h.
Using the rule for calculating the range element associated with 0 we obtain
h(0) = 5(0)2 - 7 = - 7.
h(0) = - 7
60.
If g is a function whose rule is g(x) = 4x2
- 6x + 3, what is g(1)?
Answer:
g(1) is the unique range element associated with the domain element 1 by the
function g.
Using the rule for calculating the range element associated with 1 we obtain
h(1) = 4(1)2 - 6(1) + 3 = 1.
g(1) = 1
62.
If h is a function whose rule is h(x) = 5x2
- 7, what is h(- 2)?
Answer:
h(- 2) is the unique range element associated with the domain element - 2
by the function h.
Using the rule for calculating the range element associated with - 2 we obtain
h(- 2) = 5(- 2)2 - 7 = 13.
h(- 2) = 13