Question 1

A car rental company charges a flat fee of $$50 plus 0.20 $$per mile driven. Which of the following equations best models the total cost $$C as a $$function of miles driven $$m$$?

Accepted Answer

$$C = 0.20m + 50$$

Question 2

Given the points $$(2, 5)$$ and $$(6, 13)$$, what is the slope of the line passing through them?

Accepted Answer

$$m = 2$$

Question 3

Which of the following equations is the equation of a line in point-slope form passing through $$(1, -3)$$ with a slope of $$4$$?

Accepted Answer

$$y + 3 = 4(x - 1)$$

Question 4

Which of the following best describes a function?

Accepted Answer

Each input has exactly one output.

Question 5

If $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$f(-2) = 15$$

Question 6

Which of the following graphs represents a function?

Accepted Answer

A graph that passes the vertical line test.

Question 7

Given $$f(x) = 3x - 2$$ and $$g(x) = x^2$ + 1$$, what is $$(f \circ g)(2)$$?

Accepted Answer

$$(f \circ g)(2) = 6$$

Question 8

Which of the following is the inverse of the function $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 5}{2}$$

Question 9

A company’s profit $$P (in $$thousands of dollars) as a function of time $$t (in $$years) is modeled by $$P(t) = -2t^2$ + 8t + 10. $$What is the maximum profit, and after how many years does it occur?

Accepted Answer

Maximum profit is $$18$$ thousand dollars after $$2$$ years.

Question 10

Which of the following best describes the domain of the function $$f(x) = \sqrt{5 - x}$$?

Accepted Answer

$$x \leq 5$$

Question 11

If $$f(x) = x^2$ and g(x) = x + 1$, what is f(g(3$$))$$?

Accepted Answer

$$16$$

Question 12

Which of the following is the equation of a line parallel to $$y = -3x + 7$$ and passing through $$(2, 4)$$?

Accepted Answer

$$y = -3x + 10$$

Question 13

A function $$f is $$defined as $$f(x) = \frac{1}{x-2}. $$What is the domain of $$f$$?

Accepted Answer

$$x 
eq 2$$

Question 14

Which of the following is the correct formula for the average rate of change of $$f(x)$$ from $$x = a to$$ $$x = b$$?

Accepted Answer

$$\frac{f(b) - f(a)}{b - a}$$

Question 15

If $$f(x) = |x - 3|$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$0$$

Question 16

Which of the following is the equation of a line perpendicular to $$y = 2x - 5$$ and passing through $$(0, 1)$$?

Accepted Answer

$$y = -\frac{1}{2}x + 1$$

Question 17

Which of the following is NOT a function?

Accepted Answer

A relation where one input has two different outputs.

Question 18

If $$f(x) = 2x + 1$$ and $$f^{-1}(x$$)$$ is its inverse, what is f$$^{-1}$$(7)$$?

Accepted Answer

$$3$$

Question 19

A population of bacteria triples every hour. If the initial population is $$100$$, which function models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 100 \cdot 3^t$$

Question 20

Which of the following best describes the range of the function $$f(x) = x^2$ - 4$$?

Accepted Answer

$$y \geq -4$$

Precalculus Study Guide: Graphs and Functions

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