A function $f(x)$ is one-to-one if $f(x_1) \neq f(x_2)$ whenever $x_1 \neq x_2$

Question 1

Which of the following transformations will shift the graph of $f(x)$ vertically upward by $c$ units?

Accepted Answer

$f(x) + c$

Question 2

Given $f(x) = 2\sin(3(x - \frac{\pi}{4})) + 1$, what is the amplitude of the function?

Accepted Answer

$2$

Question 3

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

Accepted Answer

A function $f(x)$ is one-to-one if $f(x_1) 
eq f(x_2)$ whenever $x_1 
eq x_2$

Question 4

What is the domain of $\cos^{-1}(x)$?

Accepted Answer

$[-1, 1]$

Question 5

What is the range of $\cos^{-1}(x)$?

Accepted Answer

$[0, \pi]$

Question 6

If $f(x)$ is invertible, which of the following must be true?

Accepted Answer

$f$ is one-to-one

Question 7

Given $f(x) = x^3 + 2$, find $f^{-1}(x)$.

Accepted Answer

$f^{-1}(x) = \sqrt[3]{x - 2}$

Question 8

Which transformation reflects the graph of $f(x)$ about the $y$-axis?

Accepted Answer

$f(-x)$

Question 9

Suppose $f(x) = \sin(x)$. Which property changes if we consider $f(x) + c$ for $c > 0$?

Accepted Answer

The $y$-intercept

Question 10

If $f(x) = 3x - 5$, what is $f^{-1}(x)$?

Accepted Answer

$f^{-1}(x) = \frac{x + 5}{3}$

Question 11

Which transformation compresses the graph of $f(x)$ horizontally by a factor of $c$ ($c > 1$)?

Accepted Answer

$f(cx)$

Question 12

Given $f(x) = \sin(x)$, what is the period of $f(x) = \sin(2x)$?

Accepted Answer

$\pi$

Question 13

Which of the following is NOT a necessary condition for a function to have an inverse?

Accepted Answer

The function must be even

Question 14

If $f(x) = |x|$, does $f$ have an inverse? Why or why not?

Accepted Answer

No, because $f(x)$ is not one-to-one

Question 15

Given $f(x) = A\sin(B(x - w)) + C$, what is the formula for the period of the function?

Accepted Answer

$\frac{2\pi}{|B|}$

Question 16

Which transformation reflects the graph of $f(x)$ about the $x$-axis?

Accepted Answer

$-f(x)$

Transformations and Inverses of Functions in Precalculus

Study Guide - Practice Questions