Question 1

Which of the following best describes a relation in mathematics?

Accepted Answer

A connection between two values, often represented as pairs $$(x, y).$$

Question 2

What is the defining property of a function?

Accepted Answer

Each input has at most one output.

Question 3

Given the set of ordered pairs $$\{(-2,2), (1,4), (3,-2), (1,1)\}$$, is this a function?

Accepted Answer

No, because the input $$1 is $$paired with two different outputs.

Question 4

Which test can be used to determine if a graph represents a function?

Accepted Answer

Vertical Line Test

Question 5

If a vertical line passes through more than one point on a graph, what does this indicate?

Accepted Answer

The graph does not represent a function.

Question 6

Consider the graph of $$y = x^2$. Does this graph represent a function?

Accepted Answer

Yes, because each input $$x$$ has exactly one output $$y.$$

Question 7

Which of the following sets of ordered pairs represents a function?

Accepted Answer

$$\{(1,2), (2,3), (3,4), (4,5)\}$$

Question 8

A business tracks the number of products sold ($$x) $$and the revenue generated ($$y). If $$each number of products sold corresponds to only one revenue value, what type of mathematical object is this?

Accepted Answer

A function

Question 9

Which scenario below is NOT a function?

Accepted Answer

A vending machine that gives two different snacks for the same button press.

Question 10

If a graph fails the vertical line test, which of the following is true?

Accepted Answer

It is not a function.

Question 11

Suppose a graph passes the vertical line test everywhere except at $$x = 2$$, where a vertical line crosses the graph at two points. What does this mean?

Accepted Answer

The graph is not a function because $$x = 2$$ has two outputs.

Question 12

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

Accepted Answer

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

Question 13

A company records the number of employees ($$x) $$and the total payroll ($$y). If $$each number of employees corresponds to only one payroll amount, what does this relationship represent?

Accepted Answer

A function

Question 14

Which of the following graphs would NOT pass the vertical line test?

Accepted Answer

A circle centered at the origin

Question 15

If a graph passes the vertical line test, which of the following statements is true?

Accepted Answer

Each input value has at most one output value.

Introduction to Functions and Their Graphs

Study Guide - Practice Questions

Study Guide - Flashcards