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 $$f(x) = |x|$$, which of the following statements is TRUE?

Accepted Answer

The function is even.

Question 3

What is the range of the function $$f(x) = x^2$?

Accepted Answer

$$[0, \infty)$$

Question 4

Which of the following functions is decreasing on $$(-\infty, 0)$$ and increasing on $$(0, \infty)$$?

Accepted Answer

$$f(x) = x^2$

Question 5

A doctor charges according to the following rule: Up to 6 minutes costs $$50, over 6 and up to 15 minutes costs 80$$, and over 15 minutes costs $$80 plus 5 $$per minute above 15 minutes. Which of the following piecewise functions correctly models the cost $$C(t)$$ for $$t$$ minutes?

Accepted Answer

$$C(t) = \begin{cases} 50 & 0  15 \end{cases}$$

Question 6

Given $$f(x) = \frac{1}{x}$$, which of the following is TRUE?

Accepted Answer

The function is undefined at $$x = 0.$$

Question 7

For the piecewise function $$f(x) = \begin{cases} x^3$ & -2 \leq x \u003c 1 \ 3x + 2 & 1 \leq x \leq 4 \end{cases}$$, what is $$f(3)$$?

Accepted Answer

$$11$$

Question 8

Which of the following best describes the range of the function $$f(x) = x^3$?

Accepted Answer

$$(-\infty, \infty)$$

Question 9

Given the function $$f(x) = 2x + 5$$ for $$-3 \leq x  0$$, what is $$f(-2)$$?

Accepted Answer

$$1$$

Question 10

Which of the following is the correct piecewise definition for $$f(x) = |3x-2|$$?

Accepted Answer

$$f(x) = 3x-2$$ for $$x \geq \frac{2}{3}$$, $$f(x) = -(3x-2)$$ for $$x \u003c \frac{2}{3}$$

Question 11

For the function $$f(x) = \sqrt[3]{x}$$, which of the following is TRUE?

Accepted Answer

The range is $$(-\infty, \infty).$$

Question 12

Given the piecewise function $$f(x) = \begin{cases} -3x & x  -1 \end{cases}$$, what is $$f(0)$$?

Accepted Answer

$$1$$

Question 13

Which of the following functions is neither even nor odd?

Accepted Answer

$$f(x) = x + 1$$

Question 14

For the function $$f(x) = |x|$$, what is the $$x-$$intercept?

Accepted Answer

$$(0, 0)$$

Question 15

Which of the following best describes the behavior of $$f(x) = \frac{1}{x} as$$ $$x$$ approaches $$0$$ from the right?

Accepted Answer

$$f(x)$$ approaches $$\infty$$

Question 16

Given $$f(x) = \begin{cases} \frac{1}{x} & x \u003c 0 \ \sqrt[3]{x} & x \geq 0 \end{cases}$$, what is $$f(-2)$$?

Accepted Answer

$$-\frac{1}{2}$$

Question 17

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

Accepted Answer

$$f(x) = 2$$

Question 18

For the function $$f(x) = x^2$ - 3$$ for $$x \geq 1$$, what is the $$y-$$intercept?

Accepted Answer

There is no $$y-$$intercept.

Question 19

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

Accepted Answer

$$[0, \infty)$$

Question 20

Given the function $$f(x) = x^3$, which of the following statements is TRUE?

Accepted Answer

The function is odd.

Functions and Their Graphs: Library and Piecewise-Defined Functions

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