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

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

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 $x$?

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

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

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

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

It can have sharp corners or jumps.

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

Accepted Answer

$f(0) = 0$

Question 3

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

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

Accepted Answer

$x = 0$ and $x = 3$

Question 6

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

Accepted Answer

The graph with a parabola for $x < 2$ 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

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

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: $f(x) = \left\{ \begin{array}{ll} 2x & x \leq 3 \ 6 + 3(x-3) & x > 3 \end{array} ight.$, 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 $f(x) = \left\{ \begin{array}{ll} x^2 & x < 2 \ -3x + 12 & x \geq 2 \end{array} ight.$, 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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