Q: A trucking company charges $$0.50 per mile for the first 100 miles, 0.40 $$per mile for the next 300 miles, and $0.20 per mile for any distance in excess of 400 miles. What is the charge per pound for a haul of 350 miles?

$$0.50 \times 100 + 0.40 \times 250 = 50$$ + $$100 = 150$

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 graph of $$f(x) = x^2$ is symmetric with respect to which axis or point?

Accepted Answer

The y-axis

Question 3

Which function from the library is an odd function and is increasing on $$(-\infty, \infty)$$?

Accepted Answer

$$f(x) = x^3$

Question 4

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

Accepted Answer

$$[0, \infty)$$

Question 5

A trucking company charges $$0.50 per mile for the first 100 miles, 0.40 $$per mile for the next 300 miles, and $0.20 per mile for any distance in excess of 400 miles. What is the charge per pound for a haul of 350 miles?

Accepted Answer

$$0.50 	imes 100 + 0.40 	imes 250 = 50$$ + $$100 = 150$

Question 6

Which of the following is the correct piecewise definition for the absolute value function $$f(x) = |x|$$?

Accepted Answer

$$f(x) = x$$ for $$x \geq 0$$; $$f(x) = -x$$ for $$x \u003c 0$$

Question 7

Which function has a domain of all real numbers except $$x = 0$$ and no intercepts?

Accepted Answer

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

Question 8

The greatest integer function $$f(x) = \lfloor x \rfloor is $$also known as:

Accepted Answer

The step function

Question 9

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

Accepted Answer

It is an odd function

Question 10

Given the piecewise function $$f(x) = \begin{cases} 2x+1 & 	ext{if } x \u003c 0 \ x^2$ & 	ext{if } x \geq 0 \end{cases}$$, what is $$f(-3)$$?

Accepted Answer

$$2(-3) + 1 = -5$$

Question 11

Which function from the library is constant for all $$x$$?

Accepted Answer

$$f(x) = b$$

Question 12

For the function $$f(x) = |x|$$, on which interval is the function decreasing?

Accepted Answer

$$(-\infty, 0)$$

Question 13

Which of the following is true about the graph of $$f(x) = x^3$?

Accepted Answer

It is symmetric with respect to the origin

Question 14

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

Accepted Answer

$$(0, 0)$$

Question 15

Which of the following best describes the range of the greatest integer function $$f(x) = \lfloor x \rfloor$$?

Accepted Answer

All integers

Question 16

A piecewise-defined function $$g(x) is $$given by $$g(x) = \begin{cases} x+2 & x \u003c 1 \ 3 & x \geq 1 \end{cases}. $$What is the range of $$g(x)$$?

Accepted Answer

$$(-\infty, 3]$$

Question 17

Which function is neither even nor odd?

Accepted Answer

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

Question 18

For the reciprocal function $$f(x) = \frac{1}{x}$$, on which intervals is the function decreasing?

Accepted Answer

$$(-\infty, 0)$$ and $$(0, \infty)$$

Question 19

Which of the following is a real-world application of a piecewise-defined function?

Accepted Answer

The cost of a cell phone plan that charges a flat rate for the first 100 minutes and a different rate for additional minutes

Question 20

If $$f(x) = \sqrt{x}$$, what is the absolute minimum value of $$f(x)$$ and at what $$x$$ does it occur?

Accepted Answer

Minimum value is $$0 at$$ $$x = 0$$

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

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