Q: A car rental company charges a base fee plus a per-mile rate. If the cost function is $$f(x) = 25 + 0.20x$$, where $$x is $$the number of miles driven, what is the cost to drive 150 miles?

$$f(150) = 25 + 0.20 \times 150 = 55$$

Q: Given $$f(x) = x^2$ - 3x + 2$$, find $$f(4).$$

$$f(4) = 4^2$ - 3 \times 4 + 2 = 6$$

Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each element in the domain is paired with exactly one element in the range.

Question 2

Given the set of ordered pairs $$\{(1, 4), (2, 5), (3, 6), (4, 7)\}$$, which of the following is true?

Accepted Answer

The relation is a function because no two ordered pairs have the same first element.

Question 3

Which of the following relations is NOT a function?

Accepted Answer

$$\{(2, 3), (2, 5), (4, 7)\}$$

Question 4

A car rental company charges a base fee plus a per-mile rate. If the cost function is $$f(x) = 25 + 0.20x$$, where $$x is $$the number of miles driven, what is the cost to drive 150 miles?

Accepted Answer

$$f(150) = 25 + 0.20 	imes 150 = 55$$

Question 5

Which of the following graphs passes the vertical line test and therefore represents a function?

Accepted Answer

A straight line with positive slope.

Question 6

Given $$f(x) = x^2$ - 3x + 2$$, find $$f(4).$$

Accepted Answer

$$f(4) = 4^2$ - 3 	imes 4 + 2 = 6$$

Question 7

What is the domain of the function $$f(x) = \frac{1}{x-5}$$?

Accepted Answer

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

Question 8

If $$f(x) = \sqrt{x-2}$$, what is the domain of $$f$$?

Accepted Answer

$$[2, \infty)$$

Question 9

Given $$f(x) = x^2$ and g(x) = 2x + 1$, find (f+g)(3$$)$$.

Accepted Answer

$$(f+g)(3) = f(3) + g(3) = 9 + 7 = 16$$

Question 10

Which of the following best describes the difference quotient for a function $$f(x)$$?

Accepted Answer

$$\frac{f(x+h) - f(x)}{h}$$

Question 11

Suppose $$f(x) = x^2$ and g(x) = x + 1$. What is $$\left(\frac{f}{g}\right)(2)$$?

Accepted Answer

$$\frac{f(2)}{g(2)} = \frac{4}{3}$$

Question 12

A piecewise-defined function is used to model a parking fee: $$f(x) = \begin{cases} 0 & x \leq 1 \ 2(x-1) & x \u003e 1 \end{cases}$$, where $$x is $$the number of hours parked. What is the fee for parking 3 hours?

Accepted Answer

$$f(3) = 2(3-1) = 4$$

Question 13

Which of the following is a correct interpretation of the vertical line test?

Accepted Answer

A graph represents a function if and only if every vertical line intersects the graph at most once.

Question 14

Given $$f(x) = 2x + 1$$ and $$g(x) = x^2$, find (f$$ \cdot g)(-2)$$.

Accepted Answer

$$(f \cdot g)(-2) = f(-2) \cdot g(-2) = (-3) \cdot 4 = -12$$

Question 15

If $$f(x) = \sqrt{9-x}$$, what is the domain of $$f$$?

Accepted Answer

$$(-\infty, 9]$$

Question 16

A hospital uses the function $$f(x) = 100 + 50x to $$model the cost (in dollars) of $$x$$ physical therapy sessions. What is the cost for 6 sessions?

Accepted Answer

$$f(6) = 100 + 50 	imes 6 = 400$$

Question 17

Given $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, find $$(f-g)(-1).$$

Accepted Answer

$$(f-g)(-1) = f(-1) - g(-1) = ((-1)^2$ - 4) - (-1 + 2) = (1 - 4) - 1 = -3 - 1 = -4$$

Question 18

Which of the following is the correct domain for the function $$f(x) = \frac{1}{\sqrt{x-1}}$$?

Accepted Answer

$$(1, \infty)$$

Functions and Their Graphs: Precalculus Study Notes

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