Q: A tax system on the planet Sarnun charges 5% on the first $$28,000 and 7% on the amount above 28$$,000. Which piecewise-defined function describes the tax $$T(x)$$ owed on an income $$x$$?

$$T(x) = \left\{ \begin{array}{ll} 0.05x & x \leq 28,000 \\ 0.05 \times 28,000 + 0.07(x - 28,000) & x \u003e 28,000 \end{array} \right.$$

Q: Given the graph in $$image_3$$, which of the following is the correct rule for the function?

$$f(x) = \left\{ \begin{array}{ll} -x + 3 & x = -3 \\ 1 & x \neq -3 \end{array} \right.$$

Question 1

Which of the following best describes a piecewise-defined function?

Accepted Answer

A function that is defined by more than one equation, each applying to a different part of the domain.

Question 2

Given the piecewise-defined function $$f(x) = \left\{ \begin{array}{ll} x^2$ & x \u003c 2 \ -3x + 12 & x \geq 2 \end{array} ight.$$, what is $$f(0)$$?

Accepted Answer

$$f(0) = 0$$

Question 3

Evaluate $$f(4)$$ for the function $$f(x) = \left\{ \begin{array}{ll} x^2$ & x \u003c 2 \ -3x + 12 & x \geq 2 \end{array} ight..$$

Accepted Answer

Question 4

For the function $$f(x) = \left\{ \begin{array}{ll} -x + 3 & x = -3 \ 1 & x 
eq -3 \end{array} ight.$$, what is $$f(-3)$$?

Accepted Answer

$$f(-3) = 6$$

Question 5

Given the piecewise-defined function $$f(x) = \left\{ \begin{array}{ll} x^2$ & x \u003c 2 \ -3x + 12 & x \geq 2 \end{array} ight.$$, find the $$x-$$intercept(s).

Accepted Answer

$$x = 0$$ and $$x = 3$$

Question 6

Which graph best represents the function $$f(x) = \left\{ \begin{array}{ll} x^2$ & x \u003c 2 \ -3x + 12 & x \geq 2 \end{array} ight.$$?

Accepted Answer

The graph with a parabola for $$x \u003c 2$$ and a straight line for $$x \geq 2 (as in$$ $$image_4).$$

Question 7

A tax system on the planet Sarnun charges 5% on the first $$28,000 and 7% on the amount above 28$$,000. Which piecewise-defined function describes the tax $$T(x)$$ owed on an income $$x$$?

Accepted Answer

$$T(x) = \left\{ \begin{array}{ll} 0.05x & x \leq 28,000 \ 0.05 	imes 28,000 + 0.07(x - 28,000) & x \u003e 28,000 \end{array} ight.$$

Question 8

If a person on Sarnun earns $30,000, how much tax do they owe according to the piecewise-defined tax function?

Accepted Answer

$$1,540$$

Question 9

For the function $$f(x) = \left\{ \begin{array}{ll} -x + 3 & x = -3 \ 1 & x 
eq -3 \end{array} ight.$$, what is the $$y-$$intercept?

Accepted Answer

$$y = 1$$

Question 10

Which of the following is NOT a characteristic of a piecewise-defined function?

Accepted Answer

It is always continuous everywhere.

Question 11

Given the graph in $$image_3$$, which of the following is the correct rule for the function?

Accepted Answer

$$f(x) = \left\{ \begin{array}{ll} -x + 3 & x = -3 \ 1 & x 
eq -3 \end{array} ight.$$

Question 12

A piecewise-defined function is used to model a parking fee: $$f(x) = \left\{ \begin{array}{ll} 2x & x \leq 3 \ 6 + 3(x-3) & x \u003e 3 \end{array} ight.$$, where $$x is $$the number of hours parked. What is the fee for 5 hours?

Accepted Answer

$$10$$

Question 13

Which of the following real-world scenarios can be modeled by a piecewise-defined function?

Accepted Answer

A cell phone plan that charges a flat rate for the first 100 minutes and a per-minute rate after that.

Question 14

If $$f(x) = \left\{ \begin{array}{ll} x^2$ & x \u003c 2 \ -3x + 12 & x \geq 2 \end{array} ight.$$, what is $$f(2)$$?

Accepted Answer

$$f(2) = 6$$

Question 15

Which of the following statements is true about the graph of a piecewise-defined function?

Accepted Answer

It can have sharp corners or jumps.

Piecewise-Defined Functions: Concepts, Evaluation, Graphs, and Applications

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