Question 1

Which of the following statements correctly describes the x-intercepts of a function $$f(x)$$?

Accepted Answer

They are the x-values where $$f(x) = 0.$$

Question 2

Given the graph of a function $$f(x)$$ defined on $$[a, b]$$ and ranging from $$c to$$ $$d$$, what is the domain and range of $$f(x)$$?

Accepted Answer

Domain: $$[a, b]$$, Range: $$[c, d]$$

Question 3

A function $$f(x) is $$increasing on an interval if:

Accepted Answer

The values of $$f(x)$$ get larger as $$x$$ increases.

Question 4

Suppose $$f(x)$$ changes from increasing to decreasing at $$x = c. $$What does this imply about $$f(x) at$$ $$x = c$$?

Accepted Answer

$$f(x)$$ has a relative maximum at $$x = c.$$

Question 5

Which of the following is true for an even function $$f(x)$$?

Accepted Answer

$$f(-x) = f(x)$$ for all $$x in $$the domain.

Question 6

Which test can be used to determine if a graph represents a function?

Accepted Answer

Vertical Line Test

Question 7

Given $$f(x) = rac{1}{x-2}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x 
eq 2$$

Question 8

If $$f(x) = rac{x^2$-4}{x-2}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x 
eq 2$$

Question 9

Which of the following equations represents a function?

Accepted Answer

$$y = x^3$ + 2x$$

Question 10

A function $$f(x) is $$odd if:

Accepted Answer

$$f(-x) = -f(x)$$ for all $$x in $$the domain.

Question 11

Given the function $$f(x) = rac{1}{oot{3}{x}}$$, what is the domain of $$f(x)$$?

Accepted Answer

All real numbers

Question 12

Which of the following is the correct interpretation of $$f(x) in $$function notation?

Accepted Answer

$$f(x)$$ means the value of the function $$f at$$ $$x$$

Question 13

If $$f(x) = x^2$ and g(x) = x + 1$, what is the value of f(g(2$$))$$?

Accepted Answer

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

Question 14

Which of the following is the difference quotient for a function $$f(x)$$?

Accepted Answer

$$\frac{f(x+h) - f(x)}{h}$$

Question 15

Which of the following describes a relation that is NOT a function?

Accepted Answer

Some elements in the domain correspond to more than one element in the range.

Question 16

Given two lines with slopes $$m_1$$ and $$m_2$$, which condition must be true for the lines to be perpendicular?

Accepted Answer

$$m_1$$ $$m_2 = -1$

Question 17

Which of the following is the equation of a line parallel to $$y = 3x + 2$$ and passing through the point $$(1, 4)$$?

Accepted Answer

Question 18

Which of the following is the equation of a line perpendicular to $$y = -2x + 5$$ and passing through $$(0, 3)$$?

Accepted Answer

$$y = \frac{1}{2}x + 3$$

Question 19

A rational function $$f(x) = \frac{p(x)}{q(x)} is $$undefined when:

Accepted Answer

$$q(x) = 0$$

Precalculus Study Guide: Functions, Graphs, and Linear Relationships

Study Guide - Practice Questions