Question 1

Given the set of ordered pairs $$\{(2, 10), (3, 10), (4, 20), (5, 30), (6, 40)\}$$, is this relation a function?

Accepted Answer

Yes, because each input value has only one output value.

Question 2

Which of the following equations represents $$y as a $$function of $$x$$?

Accepted Answer

$$y = x^2$ - 3$$

Question 3

A hospital tracks the temperature of a patient every hour. Is the relationship between time (input) and temperature (output) a function?

Accepted Answer

Yes, because each time corresponds to exactly one temperature reading.

Question 4

Which graph below passes the vertical line test and represents a function?

Accepted Answer

A graph of $$y = x^3$ - 2x + 1.$$

Question 5

Given the function $$f(x) = x^2$ + 3x - 4$$, what is $$f(2)$$?

Accepted Answer

$$6$$

Question 6

Given the table below, what is the value of $$g(3)$$?

$$x$$ | $$y$$
---|---
-1 | 2
-5 | 11
8 | 4
0 | 12
-2 | -2

Accepted Answer

Not defined

Question 7

Which of the following best describes the domain of $$f(x) = \sqrt{7-x}$$?

Accepted Answer

$$(-\infty, 7]$$

Question 8

A cell phone company charges $$C(g)$$ dollars for $$g$$ gigabytes of data as follows:

$$C(g) = \begin{cases} 20, & 0 \leq g \leq 2 \ 20 + 10(g-2), & g \u003e 2 \end{cases}$$

What is the cost for using 4 gigabytes of data?

Accepted Answer

$$40$$

Question 9

Given $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = f(3) = 9$$

Question 10

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 11

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 12

Given $$f(x) = x^2$ + 2x$$, compute the difference quotient $$\frac{f(x+h) - f(x)}{h}.$$

Accepted Answer

$$2x + h + 2$$

Question 13

Which transformation describes $$g(x) = f(x) + 3$$ compared to $$f(x)$$?

Accepted Answer

A vertical shift up by 3 units.

Question 14

Given the function $$f(x) = 2x^2$ + 1$$, what is the effect of the transformation $$g(x) = -2x^2$ + 1$$?

Accepted Answer

Vertical reflection and vertical stretch.

Question 15

Given $$f(x) = x^2$ and g(x) = 2f(x$$)$$, what is the effect on the graph?

Accepted Answer

Vertical stretch by a factor of 2.

Question 16

Given $$f(x) = x^2$ and g(x) = f(2x$$)$$, what is the effect on the graph?

Accepted Answer

Horizontal compression by a factor of $$\frac{1}{2}.$$

Question 17

Given $$f(x) = x^2$ + 2x$$ and $$f(-x) = x^2$ - 2x$$, is $$f(x)$$ even, odd, or neither?

Accepted Answer

Neither

Question 18

Given the table below, what is $$f^{-1}(4$$)$$?

x$ | f(x$$)$$
---|---
1 | 4
2 | 3
3 | 1
4 | 2

Accepted Answer

$$1$$

Question 19

Given $$f(x) = \frac{2}{x-3} + 4$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{2}{x-4} + 3$$

Functions and Their Properties: A College Algebra Study Guide

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