Q: Suppose a real-world scenario: A taxi company charges a flat fee of $$\3$ for the first mile and $$\$$2$$ for each additional mile. Which piecewise function best models the cost $$C(x)$$ for $$x$$ miles, where $$x \geq 0$$?

$$C(x) = \begin{cases} 3, & 0 \leq x \leq 1 \\ 2(x-1) + 3, & x \u003e 1 \end{cases}$$

Q: Which of the following best describes the end behavior of $$f(x) = \begin{cases} 1, & x 3 \end{cases} as$$ $$x \to -\infty$$ and $$x \to \infty$$?

$$f(x) \to 1 as$$ $$x \to -\infty$$ and $$f(x) \to -6 as$$ $$x \to \infty$$

Q: A medical test result is interpreted as follows: If $$x 100$$, the patient is in danger. Which piecewise function $$P(x)$$ best models this scenario, where $$x is $$the test result?

$$P(x) = \begin{cases} \text{Healthy}, & x 100 \end{cases}$$

Q: A company pays its employees according to the following rule: $$\15$ per hour for the first 8 hours, and $$\$$22.50$$ per hour for every hour above 8 in a day. Which piecewise function $$W(h)$$ models the daily wage for $$h$$ hours worked?

$$W(h) = \begin{cases} 15h, & 0 \leq h \leq 8 \\ 15 \times 8 + 22.5(h-8), & h \u003e 8 \end{cases}$$

Question 1

Given the piecewise function $$h(x) = \begin{cases} -x-3, & x \leq -4 \ x+3, & x \u003e -1 \end{cases}$$, which of the following best describes the domain of $$h(x)$$?

Accepted Answer

$$(-\infty, -4] \cup (-1, \infty)$$

Question 2

For the function $$f(x) = \begin{cases} 1, & x  3 \end{cases}$$, what is the value of $$f(0)$$?

Accepted Answer

$$-1$$

Question 3

Which of the following is the correct graph for $$h(x) = \begin{cases} -x-3, & x \leq -4 \ x+3, & x \u003e -1 \end{cases}$$?

Accepted Answer

A graph with two rays: one with negative slope starting at $$(-4, 1)$$ and extending left, and one with positive slope starting at $$(-1, 2)$$ and extending right, with an open circle at $$(-1, 2).$$

Question 4

If $$f(x) = \begin{cases} 1, & x  3 \end{cases}$$, what is the range of $$f(x)$$?

Accepted Answer

$$\{1\} \cup [-4, 2] \cup \{-6\}$$

Question 5

Which of the following statements is true about the graph of $$f(x) = \begin{cases} 1, & x  3 \end{cases}$$?

Accepted Answer

There is a jump discontinuity at $$x = -3$$ and $$x = 3.$$

Question 6

Given $$h(x) = \begin{cases} -x-3, & x \leq -4 \ x+3, & x \u003e -1 \end{cases}$$, what is the value of $$h(-5)$$?

Accepted Answer

$$2$$

Question 7

For the function $$f(x) = \begin{cases} 1, & x  3 \end{cases}$$, which interval describes where $$f(x) is $$decreasing?

Accepted Answer

$$-3 \u003c x \u003c 3$$

Question 8

Suppose a real-world scenario: A taxi company charges a flat fee of $$\3$ for the first mile and $$\$$2$$ for each additional mile. Which piecewise function best models the cost $$C(x)$$ for $$x$$ miles, where $$x \geq 0$$?

Accepted Answer

$$C(x) = \begin{cases} 3, & 0 \leq x \leq 1 \ 2(x-1) + 3, & x \u003e 1 \end{cases}$$

Question 9

Given $$h(x) = \begin{cases} -x-3, & x \leq -4 \ x+3, & x \u003e -1 \end{cases}$$, which of the following is true about the graph?

Accepted Answer

There is a gap in the graph between $$x = -4$$ and $$x = -1$$ where $$h(x) is $$not defined.

Question 10

A piecewise function is defined as $$g(x) = \begin{cases} 2x+1, & x \u003c 0 \ -x+4, & x \geq 0 \end{cases}. $$What is the value of $$g(-2) + g(2)$$?

Accepted Answer

$$1$$

Question 11

Which of the following best describes the end behavior of $$f(x) = \begin{cases} 1, & x  3 \end{cases} as$$ $$x 	o -\infty$$ and $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o 1 as$$ $$x 	o -\infty$$ and $$f(x) 	o -6 as$$ $$x 	o \infty$$

Question 12

A medical test result is interpreted as follows: If $$x  100$$, the patient is in danger. Which piecewise function $$P(x)$$ best models this scenario, where $$x is $$the test result?

Accepted Answer

$$P(x) = \begin{cases} 	ext{Healthy}, & x  100 \end{cases}$$

Question 13

If $$f(x) = \begin{cases} 1, & x  3 \end{cases}$$, what is $$f(-3)$$?

Accepted Answer

$$2$$

Question 14

A company pays its employees according to the following rule: $$\15$ per hour for the first 8 hours, and $$\$$22.50$$ per hour for every hour above 8 in a day. Which piecewise function $$W(h)$$ models the daily wage for $$h$$ hours worked?

Accepted Answer

$$W(h) = \begin{cases} 15h, & 0 \leq h \leq 8 \ 15 	imes 8 + 22.5(h-8), & h \u003e 8 \end{cases}$$

Piecewise Functions: Writing Equations and Graphing

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