Q: Which of the following is the correct formula for the piecewise function graphed in the first image?

$$f(x) = \begin{cases} 2 & \text{if } -5 \leq x \leq -1 \\ -2 & \text{if } -1 \u003c x \leq 2 \\ -4 & \text{if } 2 \u003c x \leq 4 \end{cases}$$

Question 1

Which of the following best describes the domain of the function $$f(x) = 3 - \sqrt{6 - 2x}$$?

Accepted Answer

$$(-\infty, 3]$$

Question 2

Given the function $$g(x) = \frac{3x + 1}{4x + 2}$$, what is the domain?

Accepted Answer

$$(-\infty, -\frac{1}{2}) \cup (-\frac{1}{2}, \infty)$$

Question 3

Which of the following functions is odd?

Accepted Answer

$$h(x) = \frac{1}{x} + 3x$$

Question 4

What is the average rate of change of $$f(x) = 2x^3$ - 1 on $$the interval $$[-2, 3]$$?

Accepted Answer

$$14$$

Question 5

Given $$f(x) = x^2$ + 6$$, $$g(x) = x - 6$$, and $$h(x) = \sqrt{x}$$, what is $$f(g(h(x)))$$?

Accepted Answer

$$x - 12\sqrt{x} + 42$$

Question 6

Which of the following is the correct formula for the piecewise function graphed in the first image?

Accepted Answer

$$f(x) = \begin{cases} 2 & 	ext{if } -5 \leq x \leq -1 \ -2 & 	ext{if } -1 \u003c x \leq 2 \ -4 & 	ext{if } 2 \u003c x \leq 4 \end{cases}$$

Question 7

What is the equation of the line passing through $$(-1, 4)$$ and $$(5, 2) in $$slope-intercept form?

Accepted Answer

$$y = -\frac{1}{3}x + \frac{11}{3}$$

Question 8

If $$f(x) = \frac{2x}{1 - x}$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x}{x + 2}$$

Question 9

A phone company charges $$C(n) = 24 + 0.1n$$, where $$n is $$the number of minutes talked. What is the rate of change and initial value?

Accepted Answer

Rate of change: $$0.1$$ dollars per minute; Initial value: $$24$$ dollars

Question 10

Given the function $$f(x) = |x|$$ reflected over the $$x-$$axis and horizontally compressed by a factor of $$\frac{1}{4}$$, what is the resulting function $$g(x)$$?

Accepted Answer

$$g(x) = -|4x|$$

Question 11

Sonya is currently 10 miles from home and is walking further away at 2 miles per hour. Which equation models her distance from home $$t$$ hours from now?

Accepted Answer

$$D(t) = 10 + 2t$$

Question 12

If the moose population in a park was 4360 in 1991 and 5880 in 1999, and the population changes linearly, what is the predicted population in 2003?

Accepted Answer

$$6640$$

Question 13

Which of the following is the correct domain for $$f(g(x)) if$$ $$f(x) = \frac{1}{x + 3}$$ and $$g(x) = \frac{2}{x - 1}$$?

Accepted Answer

$$(-\infty, \frac{1}{3}) \cup (\frac{1}{3}, 1) \cup (1, \infty)$$

Question 14

What is the equation of the line perpendicular to $$h(t) = -2t + 4$$ and passing through $$(-4, 1)$$?

Accepted Answer

$$y = \frac{1}{2}t + 3$$

Question 15

You are choosing between two prepaid cell phone plans. Plan 1 charges $$0.26$$ per minute. Plan 2 charges $$19.95$$ per month plus $$0.11$$ per minute. For what number of minutes is Plan 2 preferable?

Accepted Answer

More than $$133$$ minutes

Question 16

A private investigator requires a $$500$$ retention fee plus $$80$$ per hour. If the total fee is $$1220$$, how many hours did the investigator work?

Accepted Answer

$$9$$ hours

Question 17

Given the graphs of $$f(x)$$ and $$g(x) in $$the third image, what is $$f(g(4))$$?

Accepted Answer

$$1$$

Piecewise Functions from Graphs – Step-by-Step Guidance

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