Question 1

Given the piecewise-defined function 
$$
f(x) = \begin{cases} x-1 & 	ext{if } -4 \leq x \u003c 2 \ -2x & 	ext{if } 2 \leq x \leq 4 \end{cases}
$$
What is the domain of $$f(x)$$?

Accepted Answer

$$[-4, 4]$$

Question 2

Evaluate $$f(2)$$ for the function
$$
f(x) = \begin{cases} x-1 & 	ext{if } -4 \leq x \u003c 2 \ -2x & 	ext{if } 2 \leq x \leq 4 \end{cases}
$$

Accepted Answer

$$-4$$

Question 3

Is the function
$$
f(x) = \begin{cases} x-1 & 	ext{if } -4 \leq x \u003c 2 \ -2x & 	ext{if } 2 \leq x \leq 4 \end{cases}
$$
continuous on its domain?

Accepted Answer

No, there is a break at $$x = 2.$$

Question 4

For the greatest integer function $$f(x) = \lfloor x \rfloor$$, what is $$f(2.9)$$?

Accepted Answer

$$2$$

Question 5

Which of the following best describes the graph of the greatest integer function $$f(x) = \lfloor x \rfloor$$?

Accepted Answer

A series of horizontal steps with open circles on the right

Question 6

A tornado has a wind speed of 150 mph. Using the Fujita scale piecewise function
$$
f(x) = \begin{cases} 1 & 40 \leq x \leq 72 \ 2 & 72 \u003c x \leq 112 \ 3 & 112 \u003c x \leq 157 \ 4 & 157 \u003c x \leq 206 \ 5 & 206 \u003c x \leq 260 \end{cases}
$$
What is the Fujita scale rating for this tornado?

Accepted Answer

$$3$$

Question 7

Let $$T$$ vary directly with $$x$$, and $$T = 33$$ when $$x = 5. $$What is the value of $$T$$ when $$x = 31$$?

Accepted Answer

$$204.6$$

Question 8

Which equation represents a direct variation between $$y$$ and $$x$$?

Accepted Answer

$$y = kx$$

Question 9

Suppose $$y$$ varies directly with $$x$$ and $$y = 12$$ when $$x = 4. $$What is the constant of variation $$k$$?

Accepted Answer

$$k = 3$$

Question 10

If $$f(x) = \lfloor x \rfloor$$, which of the following is true for $$x = -1.2$$?

Accepted Answer

$$f(-1.2) = -2$$

Question 11

A piecewise function is defined as follows:
$$
f(x) = \begin{cases} 2x+1 & x \u003c 0 \ x^2$ & x \geq 0 \end{cases}
$$
What is $$f(-3) + f(2)$$?

Accepted Answer

$$7$$

Question 12

Which of the following statements about direct variation is correct?

Accepted Answer

The graph is a straight line passing through the origin.

Question 13

If $$y$$ varies directly with $$x$$ and $$y = 15$$ when $$x = 3$$, what is $$y$$ when $$x = 7$$?

Accepted Answer

$$35$$

Question 14

Which of the following is NOT a property of the greatest integer function $$f(x) = \lfloor x \rfloor$$?

Accepted Answer

It is continuous everywhere.

Question 15

A piecewise function models the cost $$C(x) of $$parking for $$x$$ hours:
$$
C(x) = \begin{cases} 5 & 0 \u003c x \leq 2 \ 5 + 2(x-2) & 2 \u003c x \leq 6 \end{cases}
$$
What is the cost for parking 4 hours?

Accepted Answer

$$9$$

Question 16

If $$f(x) = \lfloor x \rfloor$$, for which value of $$x$$ does $$f(x)$$ change from $$1 to$$ $$2$$?

Accepted Answer

$$x = 2$$

Question 17

Suppose $$y$$ varies directly with $$x$$ and inversely with $$z. If$$ $$y = 10$$ when $$x = 5$$ and $$z = 2$$, what is $$y$$ when $$x = 8$$ and $$z = 4$$?

Accepted Answer

$$8$$

Question 18

Which real-world scenario is best 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.

Piecewise-Defined Functions, Greatest Integer Function, and Direct Variation

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