Question 1

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

Accepted Answer

$$[0, \infty)$$

Question 2

Given the relation $$\{(1, 2), (3, 4), (6, 5), (8, 5)\}$$, is this relation a function?

Accepted Answer

Yes, because each domain value maps to exactly one range value.

Question 3

For the function $$f(x) = 2x$$, what is the value of $$f(-2)$$?

Accepted Answer

$$-4$$

Question 4

Which graph passes the vertical line test and represents a function?

Accepted Answer

A graph where every vertical line crosses the curve at most once.

Question 5

Given $$g(x) = 2x - 3$$, what is $$g(1)$$?

Accepted Answer

$$-1$$

Question 6

Which of the following is the range of the function $$f(x) = \sqrt{x}$$ for $$x in$$ $$[0, 9]$$?

Accepted Answer

$$[0, 3]$$

Question 7

If the graph of a function $$y = f(x)$$ crosses the x-axis at $$x = -2$$, $$x = 3$$, and $$x = 5$$, what are the x-intercepts?

Accepted Answer

$$(-2, 0), (3, 0), (5, 0)$$

Question 8

What is the y-intercept of the function $$f(x) = 0.012x^2$ - 0.2x + 8.7$$?

Accepted Answer

$$8.7$$

Question 9

Which of the following relations is NOT a function?

Accepted Answer

$$\{(1, 2), (2, 3), (1, 4)\}$$

Question 10

Given the function $$f(x) = \sqrt{x}$$ and $$g(x) = \sqrt{x} - 1$$, how is the graph of $$g(x)$$ related to the graph of $$f(x)$$?

Accepted Answer

The graph of $$g(x) is $$shifted 1 unit down.

Question 11

What is the domain of the function $$f(x)$$ shown in the graph where inputs on the x-axis extend from $$-4 to$$ $$2$$, inclusive?

Accepted Answer

$$[-4, 2]$$

Question 12

A commuter drives 40 miles to work and returns on the same route. If the average rate on the return trip is 30 mph faster than the outgoing trip, and the outgoing rate is $$x$$, which function models the total time $$T$$ spent commuting?

Accepted Answer

$$T(x) = \frac{40}{x} + \frac{40}{x+30}$$

Question 13

For the function $$f(x) = 2x$$, what is the range if the domain is $$\{-2, -1, 0, 1, 2\}$$?

Accepted Answer

$$\{-4, -2, 0, 2, 4\}$$

Question 14

Which of the following equations does NOT define $$y as a $$function of $$x$$?

Accepted Answer

$$x^2$$ + $$y^2 = 1$

Question 15

Given the graph of $$y = f(x)$$, how do you find the y-intercept?

Accepted Answer

Find the point where the graph crosses the y-axis.

Question 16

If $$f(x) = 0.012x^2$ - 0.2x + 8.7$$, what is $$f(30)$$?

Accepted Answer

$$13.5$$

Question 17

Which of the following is the correct interval notation for the set $$\{x \mid -4 \leq x \leq 2\}$$?

Accepted Answer

$$[-4, 2]$$

Question 18

If $$g(x) = 2x - 3$$, for what value of $$x is$$ $$g(x) = 1$$?

Accepted Answer

$$x = 2$$

Question 19

Which of the following statements about the vertical line test is TRUE?

Accepted Answer

If a vertical line crosses a graph more than once, the graph does not represent a function.

Study Notes: Basics of Functions and Their Graphs

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