$[\text{minimum value}, \infty)$

Question 1

What is the domain of the function $f(x) = \sqrt{x-9}$?

Accepted Answer

$[9, \infty)$

Question 2

Given $g(x) = \dfrac{x}{x^2 - 6}$, which of the following describes its domain?

Accepted Answer

$x 
eq \pm \sqrt{6}$

Question 3

Which transformation is represented by $y = f(x) + c$ for $c > 0$?

Accepted Answer

A vertical shift upward by $c$ units

Question 4

If $f(x)$ is an even function, which symmetry does its graph have?

Accepted Answer

Symmetry about the $y$-axis

Question 5

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

Accepted Answer

$(x+1)^2$

Question 6

Which of the following describes the effect of the transformation $y = f(-x)$?

Accepted Answer

Reflection about the $y$-axis

Question 7

Suppose $f(x) = \sqrt{x+1}$ and $g(x) = x^2 - 16$. What is the domain of $f+g$?

Accepted Answer

$[-1, \infty)$

Question 8

Given $f(x) = 2x^2 - 5x$, what is the range of $f(x)$?

Accepted Answer

$[	ext{minimum value}, \infty)$

Question 9

Which of the following is the correct order of operations for multiple transformations on a function?

Accepted Answer

Horizontal shifts, then stretches/compressions, then reflections, then vertical shifts

Question 10

If $f(x) = \sqrt{x}$, what is the graph of $y = -f(x)$?

Accepted Answer

The graph of $f(x)$ reflected about the $x$-axis

Question 11

Given $f(x) = \dfrac{12}{2x+4}$ and $g(x) = \sqrt{x}$, what is the domain of $f \cdot g$?

Accepted Answer

$x > 0$ and $x 
eq -2$

Question 12

Which transformation is represented by $y = f(ax)$ for $a > 1$?

Accepted Answer

Horizontal compression by a factor of $a$

Question 13

If $f(x)$ is odd, which of the following is true?

Accepted Answer

$f(-x) = -f(x)$

Question 14

Given $f(x) = x^3 - 3x^2 + 2x$, solve the inequality $f(x) \geq 0$.

Accepted Answer

$x \leq 0$ or $x = 1$ or $x \geq 2$

Question 15

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

Accepted Answer

Each $y$ in the range is paired with exactly one $x$ in the domain

Question 16

Given $f(x) = 4x+1$, $g(x) = \dfrac{x}{x-2}$, and $h(x) = \sqrt{x+3}$, what is $(f \circ g)(x)$?

Accepted Answer

$4\left(\dfrac{x}{x-2}\right) + 1$

Question 17

If $f(x) = |x|$, what is the effect of the transformation $y = 3|x|$?

Accepted Answer

Vertical stretch by a factor of 3

Question 18

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

Accepted Answer

$[2, \infty)$

Question 19

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

Accepted Answer

$9$

Question 20

Which of the following best describes the transformation $y = f(x) - c$ for $c > 0$?

Accepted Answer

Vertical shift downward by $c$ units

Study Guide: Transformations and Algebra of Functions in Precalculus

Study Guide - Practice Questions