Question 1

Given the piecewise function $$f(x) = \begin{cases} -4 & 	ext{for } x \leq -1 \ 6 & 	ext{for } x \u003e -1 \end{cases}$$, what is the value of $$f(-2)$$?

Accepted Answer

$$-4$$

Question 2

For the function $$g(x) = \begin{cases} -x + 4 & 	ext{for } 2 \leq x \u003c 6 \ 5 & 	ext{for } x \geq 6 \end{cases}$$, on which interval is $$g(x)$$ constant?

Accepted Answer

$$x \geq 6$$

Question 3

Given $$f(x) = 3x + 2$$ and $$g(x) = 5x - 4$$, what is $$(f + g)(x)$$?

Accepted Answer

$$8x - 2$$

Question 4

Given $$f(x) = 3x + 2$$ and $$g(x) = 5x - 4$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$3(5x - 4) + 2$$

Question 5

What is the domain of $$\left( \dfrac{f}{g} \right)(x)$$, where $$f(x) = 3x + 2$$ and $$g(x) = 5x - 4$$?

Accepted Answer

$$x 
eq \dfrac{4}{5}$$

Question 6

If $$f(x) = x^2$ and g(x$$) = $$x^2 + 4$, how is the graph of g(x$$)$$ related to the graph of f(x$$)$$?

Accepted Answer

$$g(x) is $$shifted 4 units up from $$f(x)$$

Question 7

Suppose the time $$t$$ required to perform a task varies inversely as the number of people $$n$$ working. If it takes 9 hours for 2 bricklayers to build a wall, how long will it take 7 bricklayers to complete the same task? (Round to the nearest tenth.)

Accepted Answer

$$2.6$$ hours

Question 8

If $$y$$ varies directly as the square root of $$x$$, and $$y = 30$$ when $$x = 25$$, what is $$x$$ when $$y = 48$$?

Accepted Answer

$$x = 64$$

Question 9

Given $$f(x) = |x|$$ and $$g(x) = 3|x + 2| - 1$$, which transformation maps $$f(x) to$$ $$g(x)$$?

Accepted Answer

Shift left 2 units, stretch vertically by 3, then shift down 1 unit

Question 10

If $$y$$ varies inversely as the square of $$x$$ and $$y = 0.15$$ when $$x = 0.1$$, what is the equation relating $$x$$ and $$y$$?

Accepted Answer

$$y = \dfrac{0.015}{x^2$}$$

Question 11

Given $$f(x) = \sqrt{x}$$ and $$g(x) = -\sqrt{x} - 2$$, what is the effect of the transformation from $$f(x) to$$ $$g(x)$$?

Accepted Answer

Reflect over the $$x-$$axis and shift down 2 units

Question 12

Given $$f(x) = \dfrac{1}{x}$$ and $$g(x) = \dfrac{1}{x} - 3$$, what is the vertical asymptote of $$g(x)$$?

Accepted Answer

$$x = 0$$

Question 13

Given $$f(x) = 3x + 2$$ and $$g(x) = 5x - 4$$, what is $$(f - g)(4)$$?

Accepted Answer

$$-10$$

Question 14

For the function $$f(x) = |x|$$, which of the following describes its domain and range?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[0, \infty)$$

Question 15

Given $$f(x) = 3x + 2$$ and $$g(x) = 5x - 4$$, what is $$(g \circ f)(3)$$?

Accepted Answer

$$41$$

Question 16

Which of the following best describes the interval(s) where the function $$f(x) = -4$$ for $$x \leq -1$$ and $$f(x) = 6$$ for $$x \u003e -1 is $$increasing?

Accepted Answer

None; the function is never increasing

Question 17

If the area $$A of a $$rectangle is expressed in terms of its width $$x$$ and a fixed perimeter $$P$$, which formula is correct?

Accepted Answer

$$A = x \left( \dfrac{P}{2} - x \right)$$

Question 18

Given $$f(x) = x^2$ and g(x$$) = $$x^2 + 4$, what is g(-2$$)$$?

Accepted Answer

$$8$$

Question 19

If $$f(x) = 3x + 2$$ and $$g(x) = 5x - 4$$, what is $$\left( \dfrac{f}{g} \right)(x)$$?

Accepted Answer

$$\dfrac{3x + 2}{5x - 4}$$

College Algebra Study Guide: Piecewise Functions, Function Operations, Transformations, and Variation

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