Question 1

Which of the following sets represents the domain of the relation $$\{(0, 9.1), (10, 6.7), (20, 10.7), (30, 13.2), (40, 21.2)\}$$?

Accepted Answer

$$\{0, 10, 20, 30, 40\}$$

Question 2

Which of the following relations is NOT a function?

Accepted Answer

$$\{(2, 3), (4, 5), (2, 6)\}$$

Question 3

Given the equation $$x^2$$ + $$y^2 = 16$, does this equation define y$ as a function of x$?

Accepted Answer

No, because for some $$x$$ values there are two corresponding $$y$$ values.

Question 4

If $$f(x) = 2x - 3$$, what is $$f(4)$$?

Accepted Answer

$$5$$

Question 5

Which of the following best describes the vertical line test for functions?

Accepted Answer

If any vertical line crosses the graph more than once, the graph is not a function.

Question 6

Given the graph of $$f(x)$$, if $$f(5) = 400$$, what is the value of $$x$$ when $$f(x) = 100$$?

Accepted Answer

$$x = 9$$

Question 7

Which of the following is the correct way to identify the range of a function from its graph?

Accepted Answer

Look for all the outputs on the $$y-$$axis that correspond to points on the graph.

Question 8

A function has $$x-$$intercepts at $$(-3, 0)$$, $$(-1, 0)$$, and $$(2, 0)$$, and a $$y-$$intercept at $$(0, -6). $$Which statement is true?

Accepted Answer

The function has three $$x-$$intercepts and one $$y-$$intercept.

Question 9

Which of the following real-world scenarios can be modeled by a function?

Accepted Answer

Each person in a city has a unique social security number.

Question 10

Suppose $$g(x) = 2x - 3. $$Which of the following points lies on the graph of $$g(x)$$?

Accepted Answer

$$(2, 1)$$

Question 11

Given the relation $$\{(1, 2), (3, 4), (6, 5), (8, 5)\}$$, what is the range?

Accepted Answer

$$\{2, 4, 5\}$$

Question 12

If a graph passes the vertical line test, what does this indicate about the graph?

Accepted Answer

It represents a function.

Question 13

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

Accepted Answer

$$y^2 = x$

Question 14

If $$f(x) = 2x$$, what is the $$y-$$intercept of the graph of $$f(x)$$?

Accepted Answer

$$(0, 0)$$

Question 15

A company models its profit $$P as a $$function of the number of units sold $$x by$$ $$P(x) = 5x - 200. $$What is the profit if 60 units are sold?

Accepted Answer

$$100$$

Functions and Graphs: Basics of Functions and Their Graphs

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