Question 1

Given the piecewise function:

$$ f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases}

If$$ $$d = 3$$, $$y = 2$$, and $$x = -4$$, what is $$f(-4)$$?

Accepted Answer

$$f(-4) = -10$$

Question 2

For the same piecewise function:

$$ f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases}

If$$ $$d = 5$$, $$y = -1$$, what is $$f(0)$$?

Accepted Answer

$$f(0) = 5$$

Question 3

Suppose $$d = 2$$, $$y = 7$$, and $$x = 4 in $$the piecewise function:

$$ f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases} $$

What is $$f(4)$$?

Accepted Answer

$$f(4) = 15$$

Question 4

If $$d = -2$$, $$y = 5$$, and $$x = 0$$, what is $$f(0)$$ for the function $$f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases}$$?

Accepted Answer

$$f(0) = -2$$

Question 5

Given $$d = 1$$, $$y = 4$$, and $$x = 10$$, what is $$f(10)$$ for the function $$f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases}$$?

Accepted Answer

$$f(10) = 14$$

Question 6

If $$d = 0$$, $$y = 6$$, and $$x = -3$$, what is $$f(-3)$$ for the function $$f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases}$$?

Accepted Answer

$$f(-3) = 6$$

Question 7

For the function $$f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases}$$, if $$d = 4$$, $$y = -2$$, and $$x = 2$$, what is $$f(2)$$?

Accepted Answer

$$f(2) = 6$$

Question 8

A chemical process is modeled by the piecewise function $$f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases}$$, where $$x is $$the concentration of a reactant. If $$d = 7$$, $$y = 3$$, and the concentration $$x = 5$$, what is the output of the process?

Accepted Answer

$$f(5) = 38$$

Question 9

A medical device uses the function $$f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases} to $$determine dosage, where $$x is $$the patient's weight in kg. If $$d = 2$$, $$y = 8$$, and the patient weighs $$x = 0 kg$$, what dosage is recommended?

Accepted Answer

$$f(0) = 2$$

Question 10

Suppose $$d = 6$$, $$y = -4$$, and $$x = -2 in $$the function $$f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases}. $$What is $$f(-2)$$?

Accepted Answer

$$f(-2) = -16$$

Question 11

If $$d = 9$$, $$y = 0$$, and $$x = 1$$, what is $$f(1)$$ for the function $$f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases}$$?

Accepted Answer

$$f(1) = 9$$

Question 12

A business uses the function $$f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases} to $$calculate profit, where $$x is $$the number of units sold. If $$d = 0$$, $$y = 12$$, and $$x = 3$$, what is the profit?

Accepted Answer

$$f(3) = 12$$

Question 13

For the function $$f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases}$$, if $$d = 8$$, $$y = -5$$, and $$x = 0$$, what is $$f(0)$$?

Accepted Answer

$$f(0) = 8$$

Question 14

If $$d = 2$$, $$y = 3$$, and $$x = 7$$, what is $$f(7)$$ for the function $$f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases}$$?

Accepted Answer

$$f(7) = 17$$

Question 15

A historical event is modeled by $$f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases}$$, where $$x is $$the year since 1900. If $$d = 1$$, $$y = 0$$, and $$x = 100$$, what is $$f(100)$$?

Accepted Answer

$$f(100) = 100$$

Question 16

If $$d = 5$$, $$y = 5$$, and $$x = -1$$, what is $$f(-1)$$ for the function $$f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases}$$?

Accepted Answer

$$f(-1) = 0$$

Question 17

A real-world application uses $$f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases}$$, with $$d = 3$$, $$y = 9$$, and $$x = 0. $$What is $$f(0)$$?

Accepted Answer

$$f(0) = 3$$

Question 18

If $$d = 4$$, $$y = 2$$, and $$x = 5$$, what is $$f(5)$$ for the function $$f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases}$$?

Accepted Answer

$$f(5) = 22$$

Question 19

For the function $$f(x) = \begin{cases} d & 	ext{if } x = 0 \ dx + y & 	ext{if } x 
eq 0 \end{cases}$$, if $$d = 7$$, $$y = 1$$, and $$x = -3$$, what is $$f(-3)$$?

Accepted Answer

$$f(-3) = -20$$

Piecewise Functions: Evaluation and Applications

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