Question 1

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

Accepted Answer

Domain: $$[0, \infty)$$, Range: $$[0, \infty)$$

Question 2

The function $$f(x) = |x| is$$:

Accepted Answer

Even and symmetric with respect to the y-axis

Question 3

Which of the following statements is TRUE about the cube root function $$f(x) = \sqrt[3]{x}$$?

Accepted Answer

It is an odd function and symmetric with respect to the origin

Question 4

What is the y-intercept of the function $$f(x) = x^2$?

Accepted Answer

$$(0, 0)$$

Question 5

Which of the following functions is neither even nor odd?

Accepted Answer

$$f(x) = \sqrt{x}$$

Question 6

A piecewise-defined function is given by $$f(x) = \begin{cases} \frac{2}{3}x + 1 & 	ext{if } x \u003c 1 \ -2x + 1 & 	ext{if } x \geq 1 \end{cases}. $$What is $$f(2)$$?

Accepted Answer

$$f(2) = -3$$

Question 7

Which function has a range of all real numbers?

Accepted Answer

$$f(x) = \sqrt[3]{x}$$

Question 8

The graph of $$f(x) = |x| is$$:

Accepted Answer

A V-shaped graph opening upwards

Question 9

For the function $$f(x) = \frac{1}{x}$$, which of the following is true?

Accepted Answer

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

Question 10

Which of the following best describes the range of the piecewise function $$f(x) = \begin{cases} \frac{2}{3}x + 1 & x \u003c 1 \ -2x + 1 & x \geq 1 \end{cases}$$?

Accepted Answer

$$(-\infty, 1]$$

Question 11

Which function is increasing on its entire domain?

Accepted Answer

$$f(x) = \sqrt[3]{x}$$

Question 12

The greatest integer function $$f(x) = 	ext{int}(x) is $$best described as:

Accepted Answer

The greatest integer less than or equal to $$x$$

Question 13

Which of the following is the correct graph for the constant function $$f(x) = b$$?

Accepted Answer

A horizontal line at $$y = b$$

Question 14

Which function has an absolute minimum at $$x = 0$$?

Accepted Answer

$$f(x) = |x|$$

Question 15

A real-world application: The cost $$C (in $$dollars) to produce $$x$$ units of a product is modeled by $$C(x) = |x - 100| + 500. $$What is the minimum cost, and for how many units is it achieved?

Accepted Answer

Minimum cost is $$500 at$$ $$x = 100$$

Question 16

Which of the following is NOT a property of the cube root function $$f(x) = \sqrt[3]{x}$$?

Accepted Answer

It has an absolute minimum at $$x = 0$$

Question 17

Given the piecewise function $$f(x) = \begin{cases} \frac{2}{3}x + 1 & x \u003c 1 \ -2x + 1 & x \geq 1 \end{cases}$$, what is the $$x-$$intercept?

Accepted Answer

$$x = -\frac{3}{2}$$

Question 18

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

Accepted Answer

$$f(x) = |x|$$

Question 19

Which of the following is the correct formula for the reciprocal function?

Accepted Answer

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

Library of Functions and Piecewise-defined Functions: Study Notes for Precalculus

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