Question 1

Which of the following best describes a piecewise function?

Accepted Answer

A function defined by different formulas for different intervals of $$x$$

Question 2

Given the piecewise function $$f(x) = \begin{cases} x+3 & 	ext{if } x \u003c 3 \ 2x-1 & 	ext{if } x \geq 3 \end{cases}$$, what is $$f(4)$$?

Accepted Answer

$$f(4) = 8$$

Question 3

A function $$g(x) is $$defined as $$g(x) = \begin{cases} 2x & 	ext{if } x \leq 0 \ x^2$ & 	ext{if } x \u003e 0 \end{cases}. $$Which of the following statements is true about $$g(x)$$?

Accepted Answer

The function is linear for $$x \leq 0$$ and quadratic for $$x \u003e 0$$

Question 4

Which interval notation correctly represents the domain of a function whose graph starts at $$x = -3$$ and ends at $$x = 5$$, including both endpoints?

Accepted Answer

$$[-3, 5]$$

Question 5

If a function $$f(x) is $$increasing on the interval $$(1, 4)$$, which of the following statements is true?

Accepted Answer

For any $$x_1$$ \u003c $$x_2 in$$ $$(1, 4)$$, $$f(x_1$) \u003c f(x_2$)$$

Question 6

Given the function $$h(x) = \begin{cases} 3x-2 & 	ext{if } x \u003c 2 \ 5 & 	ext{if } x \geq 2 \end{cases}$$, what is the range of $$h(x)$$?

Accepted Answer

$$(-\infty, 5) \cup \{5\}$$

Question 7

A function $$f(x) is $$constant on the interval $$[2, 5]. $$Which of the following best describes the graph of $$f(x) on $$this interval?

Accepted Answer

A horizontal line

Question 8

Which of the following is the correct interval notation for the range of a function whose lowest $$y-$$value is $$-3$$ and highest $$y-$$value is $$0$$, not including $$0$$?

Accepted Answer

$$[-3, 0)$$

Question 9

If a function $$f(x)$$ has a relative maximum at $$x = 2$$ with $$f(2) = 5$$, which statement is true?

Accepted Answer

The function has its highest value at $$x = 2$$ compared to nearby points

Question 10

A function $$f(x) is $$decreasing on the interval $$(-5, -1). $$Which of the following is true?

Accepted Answer

For any $$x_1  f$$($$x_2$$)$$

Question 11

Given the function $$f(x) = \begin{cases} x^2$ & 	ext{if } x \u003c 0 \ 2x+1 & 	ext{if } x \geq 0 \end{cases}$$, what is $$f(-2)$$?

Accepted Answer

$$f(-2) = 4$$

Question 12

Which of the following best describes the domain of a function whose graph covers all real numbers except $$x = 1$$?

Accepted Answer

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

Question 13

A piecewise function models the cost of parking in a city: $$C(h) = \begin{cases} 2h & 	ext{if } h \leq 3 \ 6 + 1.5(h-3) & 	ext{if } h \u003e 3 \end{cases}$$, where $$h is $$hours parked. What is the cost for parking 5 hours?

Accepted Answer

$$C(5) = 9$$

Question 14

If a function $$f(x)$$ has a relative minimum at $$x = -3$$ with $$f(-3) = 1$$, what does this mean?

Accepted Answer

The function has its lowest value at $$x = -3$$ compared to nearby points

Question 15

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

Accepted Answer

$$f(1) = 4$$

Question 16

Which of the following intervals represents where a function is constant?

Accepted Answer

$$[2, 5]$$

Question 17

A function $$f(x) is $$increasing on $$(3, 5)$$, decreasing on $$(-5, -1)$$, and constant on $$(2, 3). $$Which of the following is true?

Accepted Answer

The function exhibits all three behaviors on different intervals

Question 18

Given the function $$f(x) = \begin{cases} x+1 & 	ext{if } x \u003c 0 \ 2x & 	ext{if } x \geq 0 \end{cases}$$, what is the domain and range?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(-\infty, \infty)$$

Question 19

A function $$f(x)$$ has a relative maximum at $$x = 1$$ and a relative minimum at $$x = -3. $$Which of the following best describes the graph near these points?

Accepted Answer

The graph has a valley at $$x = -3$$ and a peak at $$x = 1$$

Piecewise Functions, Increasing/Decreasing/Constant Functions, Domain & Range, and Relative Extrema

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