Square root function $y = \sqrt{x}$

$[0, \infty) \cup (-\infty, -2)$

Question 1

Which of the following best describes the domain and range of the constant function $y = c$?

Accepted Answer

Domain: $(-\infty, \infty)$; Range: $\{c\}$

Question 2

For the identity function $y = x$, which of the following statements is true?

Accepted Answer

It is increasing on $(-\infty, \infty)$.

Question 3

What is the range of the absolute value function $y = |x|$?

Accepted Answer

$[0, \infty)$

Question 4

On which interval is the absolute value function $y = |x|$ decreasing?

Accepted Answer

$(-\infty, 0)$

Question 5

Which of the following is the domain of the square root function $y = \sqrt{x}$?

Accepted Answer

$[0, \infty)$

Question 6

For the cubic function $y = x^3$, which statement is correct?

Accepted Answer

It is increasing on $(-\infty, \infty)$.

Question 7

What is the range of the cubic root function $y = \sqrt[3]{x}$?

Accepted Answer

$(-\infty, \infty)$

Question 8

Consider the piecewise function $f(x) = \begin{cases} 2x & 	ext{if } x \leq 1 \ 2 & 	ext{if } x > 1 \end{cases}$. What is the value of $f(-2)$?

Accepted Answer

$-4$

Question 9

For the piecewise function $f(x) = \begin{cases} x^2 & 	ext{if } x \geq 0 \ -x-2 & 	ext{if } x < 0 \end{cases}$, what is $f(-3)$?

Accepted Answer

$-5$

Question 10

Which function has a domain of $(-\infty, \infty)$ and a range of $(-\infty, \infty)$?

Accepted Answer

Identity function $y = x$

Question 11

Which function is increasing on $(0, \infty)$ and decreasing on $(-\infty, 0)$?

Accepted Answer

Absolute value function $y = |x|$

Question 12

If $f(x) = \sqrt{x}$, what is $f(16)$?

Accepted Answer

$4$

Question 13

Which function is not defined for negative $x$ values?

Accepted Answer

Square root function $y = \sqrt{x}$

Question 14

For the function $y = |x|$, what is the value of $y$ when $x = -7$?

Accepted Answer

$7$

Question 15

Which of the following functions is constant for all $x$?

Accepted Answer

Constant function $y = c$

Question 16

For the piecewise function $f(x) = \begin{cases} 2x & x \leq 1 \ 2 & x > 1 \end{cases}$, what is the range of $f(x)$?

Accepted Answer

$(-\infty, 2]$

Question 17

Which function's graph has a sharp 'corner' at $x = 0$?

Accepted Answer

Absolute value function $y = |x|$

Question 18

If $f(x) = x^3$, what is $f(-2)$?

Accepted Answer

$-8$

Question 19

Which function is increasing for all $x$ and has both domain and range $(-\infty, \infty)$?

Accepted Answer

Cubic root function $y = \sqrt[3]{x}$

Question 20

For the piecewise function $f(x) = \begin{cases} x^2 & x \geq 0 \ -x-2 & x < 0 \end{cases}$, what is the range of $f(x)$?

Accepted Answer

$[0, \infty) \cup (-\infty, -2)$

Fundamental Functions and Piecewise Functions in Precalculus

Study Guide - Practice Questions