Question 1

Which of the following statements correctly describes when a function $f$ has an inverse function $f^{-1}$?

Accepted Answer

A function has an inverse if and only if it is a one-to-one function.

Question 2

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

Accepted Answer

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

Question 3

Which of the following functions is NOT one-to-one?

Accepted Answer

$f(x) = x^2$ on $(-\infty, \infty)$

Question 4

If $f(x) = ax + b$ where $a 
eq 0$, what is the inverse function $f^{-1}(x)$?

Accepted Answer

$f^{-1}(x) = \frac{x-b}{a}$

Question 5

Which of the following is the correct definition of a one-to-one function?

Accepted Answer

For all $a$ and $b$, if $f(a) = f(b)$ then $a = b$.

Question 6

Consider the function $f(x) = x^2$ with domain $[0, \infty)$. What is the inverse function $f^{-1}(x)$?

Accepted Answer

$f^{-1}(x) = \sqrt{x}$

Question 7

In the rectangular coordinate system, what are the coordinates of the origin?

Accepted Answer

$(0, 0)$

Question 8

Which quadrant does the point $(-3, 4)$ lie in?

Accepted Answer

Quadrant II

Question 9

If the graph of $y = f(x)$ is symmetric about the y-axis, which of the following must be true?

Accepted Answer

Replacing $x$ by $-x$ yields an equivalent equation.

Question 10

Which of the following is the correct process to find the inverse of a one-to-one function $f$?

Accepted Answer

Solve $y = f(x)$ for $x$ in terms of $y$, then replace $y$ with $x$.

Question 11

Which of the following equations represents a function that is symmetric about the origin?

Accepted Answer

$y = x^3$

Question 12

If $f(x) = x^2 + 2x - 3$, what are the $x$-intercepts of its graph?

Accepted Answer

$x = -3$ and $x = 1$

Question 13

Which of the following is NOT a property of the inverse function $f^{-1}$?

Accepted Answer

$f^{-1}$ is always the same as $\frac{1}{f}$

Question 14

A function $f$ is defined by $f(x) = |x|$. Which statement is true about its graph?

Accepted Answer

It is symmetric about the y-axis.

Question 15

Which of the following points is in Quadrant IV of the rectangular coordinate system?

Accepted Answer

$(3, -2)$

Question 16

If $f(x)$ is a one-to-one function and $g(x)$ is also one-to-one, what can be said about the composite function $f \circ g$?

Accepted Answer

$f \circ g$ is also one-to-one.

Question 17

Which of the following is the correct way to check if a graph represents a function?

Accepted Answer

Use the vertical line test.

Question 18

If $f(x) = x^2$ is restricted to the domain $[0, \infty)$, what is the range of $f$?

Accepted Answer

$[0, \infty)$

Question 19

Which of the following is true about the graph of $y = x^2$?

Accepted Answer

It is symmetric about the y-axis.

Functions, Inverses, and Graphs in Rectangular Coordinates

Study Guide - Practice Questions