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 $$\{(-2,2), (1,4), (3,-2), (5,-2)\}$$, is this a function?

Accepted Answer

Yes, because each input is paired with only one output.

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

Accepted Answer

No, because the input $$3 is $$paired with two different outputs.

Question 7

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

Accepted Answer

A circle centered at the origin

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, is this relationship a function?

Accepted Answer

Yes, because each input ($$x) $$has only one output ($$y).$$

Question 9

Which of the following is a function?

Accepted Answer

A machine that assigns each barcode to a unique product.

Question 10

If a graph passes the vertical line test, what can you conclude?

Accepted Answer

The graph represents a function.

Question 11

Which of the following real-world scenarios is NOT a function?

Accepted Answer

A person can have multiple phone numbers.

Question 12

Given the graph of $$y = x^2$, does it represent a function?

Accepted Answer

Yes, because each $$x$$ has only one $$y.$$

Question 13

Which statement is true about the vertical line test?

Accepted Answer

If any vertical line intersects the graph at more than one point, it is not a function.

Question 14

A company records the number of employees ($$x) $$and the total payroll ($$y). If $$two different numbers of employees result in the same payroll, is this a function?

Accepted Answer

Yes, because each input ($$x) $$still has only one output ($$y).$$

Question 15

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

Accepted Answer

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

Introduction to Functions and Their Graphs

Study Guide - Practice Questions

Study Guide - Flashcards