Question 1

Which of the following best describes a relation in mathematics?

Accepted Answer

A connection between two values.

Question 2

How are relations typically represented graphically?

Accepted Answer

As pairs $$(x, y).$$

Question 3

Which statement correctly defines a function?

Accepted Answer

A function is a special type of relation where each input has at most one output.

Question 4

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

Accepted Answer

Yes, because each input has only one output.

Question 5

Which of the following sets of ordered pairs is NOT a function?

Accepted Answer

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

Question 6

What is the Vertical Line Test used for?

Accepted Answer

To determine if a graph represents a function.

Question 7

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

Accepted Answer

The graph is not a function.

Question 8

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

Accepted Answer

A graph of $$y = x^2$.

Question 9

Consider the mapping diagram: Inputs $$\{1, 2, 3\}$$, Outputs $$\{4, 5, 6\}$$, with arrows from 1 to 4, 2 to 5, and 3 to 6. Is this a function?

Accepted Answer

Yes, because each input maps to exactly one output.

Question 10

Which of the following is a real-world example of a function?

Accepted Answer

Assigning each employee ID to a single employee name.

Question 11

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

Accepted Answer

There exists at least one input with more than one output.

Question 12

Which of the following best describes the difference between a relation and a function?

Accepted Answer

A function is a relation where each input has at most one output.

Question 13

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

Accepted Answer

Yes, because it passes the vertical line test.

Question 14

Which of the following is NOT a function?

Accepted Answer

A graph where $$x = 2$$ maps to both $$y = 3$$ and $$y = -1.$$

Question 15

Which statement is true about the vertical line test?

Accepted Answer

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

Introduction to Functions and Their Graphs

Study Guide - Practice Questions