Question 1

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

Accepted Answer

$[0, \infty)$

Question 2

Given the function $f(x) = x^3$, which statement about its graph is true?

Accepted Answer

It passes through the origin and is symmetric about the origin.

Question 3

What is the range of the function $f(x) = |x|$?

Accepted Answer

$[0, \infty)$

Question 4

Which of the following is the correct graph for $f(x) = \frac{1}{x^2}$?

Accepted Answer

A graph with two branches, both above the x-axis, approaching infinity as $x$ approaches 0 from both sides.

Question 5

For the piecewise function $f(x) = \begin{cases} 2x - 2 & 	ext{if } x \geq 3 \ x^2 + 2 & 	ext{if } x < 3 \end{cases}$, what is $f(4)$?

Accepted Answer

$10$

Question 6

Which function is NOT a polynomial?

Accepted Answer

$f(x) = \frac{1}{x}$

Question 7

A chemical reaction rate is modeled by $f(x) = x^2$. If the concentration doubles, by what factor does the reaction rate increase?

Accepted Answer

It quadruples.

Question 8

Which of the following describes the end behavior of $f(x) = x^5$ as $x 	o -\infty$?

Accepted Answer

$f(x) 	o -\infty$

Question 9

The function $f(x) = \sqrt[3]{x}$ is defined for which values of $x$?

Accepted Answer

$(-\infty, \infty)$

Question 10

A medical dosage is modeled by $f(x) = |x|$. If a patient receives a dose of $-5$ mg, what is the effective dosage?

Accepted Answer

$5$ mg

Question 11

Which of the following functions has a vertical asymptote at $x=0$?

Accepted Answer

$f(x) = \frac{1}{x}$

Question 12

For the piecewise function $f(x) = \begin{cases} x^2 - 1 & x < 1 \ 3 & x = 1 \ -2x + 5 & x > 1 \end{cases}$, what is $f(2)$?

Accepted Answer

$1$

Question 13

Which function's graph is always increasing for all $x$ in its domain?

Accepted Answer

$f(x) = x$

Question 14

If $f(x) = x^4$, which of the following statements is true?

Accepted Answer

The graph is symmetric about the y-axis.

Question 15

Which function best models the depreciation of a car's value over time, assuming the value halves every year?

Accepted Answer

$f(x) = 2^{-x}$

Question 16

For the function $f(x) = \frac{1}{x^3}$, what happens as $x$ approaches $0$ from the positive side?

Accepted Answer

$f(x) 	o \infty$

Question 17

Which of the following is the correct domain for $f(x) = \sqrt[4]{x}$?

Accepted Answer

$[0, \infty)$

Question 18

A population grows according to $f(x) = x^2$. If the initial population is $3$, what is the population after doubling the input?

Accepted Answer

$36$

Question 19

Which function is an example of a rational function?

Accepted Answer

$f(x) = \frac{1}{x}$

Question 20

For the piecewise function $f(x) = \begin{cases} 2x^2 - 11 & x \leq -3 \ -2x^2 + x & -3 < x \leq -1 \ \frac{1}{3}x + 5 & x > -1 \end{cases}$, what is $f(-2)$?

Accepted Answer

$-9$

Overview of Common Functions and Their Graphs in College Algebra

Study Guide - Practice Questions

Study Guide - Flashcards