Q: Suppose your hourly wage every week is $$20.00 per hour for the first 40 hours you work, time and a half for every hour between 40 and 50 hours, and double time for every hour over 50 hours. Which of the following piecewise functions correctly models your weekly pay P(x$$)$$ as a function of hours worked x$?

$$P(x) = \begin{cases} 20x & 0 \leq x \leq 40 \\ 800 + 30(x-40) & 40 50 \end{cases}$$

Q: A company pays its employees according to the following rule: $$\15$ per hour for the first 35 hours, $$\$$22.50$$ per hour for the next 10 hours, and $$\30$ per hour for any hours above 45. Which of the following piecewise functions represents the weekly pay W(x$$)$$ for x$ hours worked?

$$W(x) = \begin{cases} 15x & 0 \leq x \leq 35 \\ 525 + 22.5(x-35) & 35 45 \end{cases}$$

Question 1

Suppose your hourly wage every week is $$20.00 per hour for the first 40 hours you work, time and a half for every hour between 40 and 50 hours, and double time for every hour over 50 hours. Which of the following piecewise functions correctly models your weekly pay P(x$$)$$ as a function of hours worked x$?

Accepted Answer

$$P(x) = \begin{cases} 20x & 0 \leq x \leq 40 \ 800 + 30(x-40) & 40  50 \end{cases}$$

Question 2

Using the pay function $$P(x)$$ from the previous question, what is your pay if you work 45 hours in a week?

Accepted Answer

$$950$$

Question 3

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

Accepted Answer

$$5$$

Question 4

For the function $$f(x) = \begin{cases} -x+1 & x  2 \end{cases}$$, what is the range of $$f(x)$$?

Accepted Answer

$$(-\infty, 1] \cup (3, \infty)$$

Question 5

Consider the piecewise function $$f(x) = \begin{cases} 2x & -5 \leq x  3 \end{cases}. $$What is $$f(5)$$?

Accepted Answer

$$1$$

Question 6

Given the function $$f(x) = \begin{cases} 2x & -5 \leq x  3 \end{cases}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$[-5, 3] \cup (3, \infty)$$

Question 7

A company pays its employees according to the following rule: $$\15$ per hour for the first 35 hours, $$\$$22.50$$ per hour for the next 10 hours, and $$\30$ per hour for any hours above 45. Which of the following piecewise functions represents the weekly pay W(x$$)$$ for x$ hours worked?

Accepted Answer

$$W(x) = \begin{cases} 15x & 0 \leq x \leq 35 \ 525 + 22.5(x-35) & 35  45 \end{cases}$$

Question 8

Refer to the first graph provided. Which real-world scenario does this graph most likely represent?

Accepted Answer

A piecewise pay function with increasing hourly rates after certain thresholds.

Question 9

Given the piecewise function $$f(x) = \begin{cases} -x+1 & x  2 \end{cases}$$, which interval is $$f(x)$$ constant?

Accepted Answer

$$-1 \leq x \u003c 2$$

Question 10

Suppose a hospital pays nurses $$\25$ per hour for up to 40 hours per week, $$\$$37.50$$ per hour for overtime up to 50 hours, and $$\50$ per hour for any hours above 50. If a nurse works 55 hours in a week, what is her total pay?

Accepted Answer

$$1875$$

Question 11

Given the function $$f(x) = \begin{cases} 2x & -5 \leq x  3 \end{cases}$$, what is $$f(-2)$$?

Accepted Answer

$$-1$$

Question 12

Which of the following best describes the range of the function $$f(x) = \begin{cases} 2x & -5 \leq x  3 \end{cases}$$?

Accepted Answer

$$[-10, -4) \cup \{-1\} \cup (-1, \infty)$$

Question 13

A piecewise function is defined as $$g(x) = \begin{cases} 3x+2 & x  4 \end{cases}. $$What is $$g(5)$$?

Accepted Answer

$$0$$

Question 14

Which of the following is NOT a possible domain for a piecewise function?

Accepted Answer

$$\{x \mid x  b\}$$

Piecewise Defined Functions – College Algebra Study Notes

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