Q: Which of the following is the correct piecewise function for the fine structure in Peach County, Georgia?

$$f(x) = \begin{cases} 0 & x \leq 55 \\ 50 + 3(x-55) & 56 \leq x \u003c 75 \\ 150 + 5(x-75) & x \geq 75 \end{cases}$$

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

A shark tooth is found to be 12 cm tall. Using the formula $$	ext{Shark length} = 0.96 	imes 	ext{height of tooth} - 0.22$$, what is the estimated length of the shark in meters?

Accepted Answer

$$11.3$$ meters

Question 3

Which of the following functions is an odd function?

Accepted Answer

$$f(x) = x^3$

Question 4

Given the piecewise function $$F(x) = \begin{cases} x^2$ & x \u003c 1 \ 2x + 1 & x \geq 1 \end{cases}$$, what is $$F(2)$$?

Accepted Answer

$$5$$

Question 5

Which of the following is the correct formula for the absolute value function?

Accepted Answer

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

Question 6

A driver is caught speeding at 70 mph in a 55 mph zone in Peach County, Georgia. Using the fine formula $$f(x) = \begin{cases} 0 & x \leq 55 \ 50 + 3(x-55) & 56 \leq x \u003c 75 \ 150 + 5(x-75) & x \geq 75 \end{cases}$$, what is the fine?

Accepted Answer

$$95$$

Question 7

Which of the following statements is true about the identity function $$f(x) = x$$?

Accepted Answer

It is an odd function.

Question 8

What is the slope of the line passing through the points $$(1, 4)$$ and $$(-3, -2)$$?

Accepted Answer

$$\frac{3}{2}$$

Question 9

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

Accepted Answer

A series of horizontal steps

Question 10

Given the piecewise function $$f(x) = \begin{cases} 2x + 1 & 1 \leq x \leq 3 \ -\frac{3}{2}x + \frac{13}{2} & 3 \u003c x \leq 5 \end{cases}$$, what is $$f(4)$$?

Accepted Answer

$$7.5$$

Question 11

Which function has a domain of $$(-\infty, \infty)$$ and a range of $$[0, \infty)$$?

Accepted Answer

$$f(x) = x^2$

Question 12

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

Accepted Answer

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

Question 13

Which of the following functions is neither even nor odd?

Accepted Answer

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

Question 14

If $$f(x) = x^3$, which of the following statements is true?

Accepted Answer

The function is odd.

Question 15

Which of the following is the correct piecewise function for the fine structure in Peach County, Georgia?

Accepted Answer

$$f(x) = \begin{cases} 0 & x \leq 55 \ 50 + 3(x-55) & 56 \leq x \u003c 75 \ 150 + 5(x-75) & x \geq 75 \end{cases}$$

Question 16

Which function is increasing on $$(-\infty, \infty)$$ and has origin symmetry?

Accepted Answer

$$f(x) = x^3$

Question 17

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

Accepted Answer

$$\{c\}$$

Question 18

Which of the following is the correct formula for the cube root function?

Accepted Answer

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

Question 19

Which function is described as a step function with jumps at every integer value of $$x$$?

Accepted Answer

$$f(x) = \lfloor x \rfloor$$

Chapter 1.6: A Library of Functions – Graphs and Properties

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