Question

example problem 3: mapping diagram
use the mapping diagram below to answer the questions about domain, range, and whether the relation is a function.
questions:

1. what is the domain of the relation?
2. what is the range of the relation?
3. is this relation a function? explain why or why not.
4. how many outputs does input 1 have?
5. if you were to graph this relation, would it pass the vertical line test? why or why not?

tek a.1.2a - domain, range, and functions
example problem 3: mapping diagram
use the mapping diagram below to answer the questions about domain, range, and whether the relation is a function.
inputs outputs
1 4
2 5
3 6

1. what is the domain of the relation?
2. what is range of the relation?
3. is this relation a function? explain why or why not.
4. if you were to graph this relation, would it pass the vertical line test? why or why not?

Explanation:

Step1: Identify domain

The domain is the set of all input values. From the mapping diagram, the input values are 1, 2, 3. So the domain is {1, 2, 3}.

Step2: Identify range

The range is the set of all output values. From the mapping diagram, the output values are 4, 5, 6. So the range is {4, 5, 6}.

Step3: Determine if function

A relation is a function if each input has exactly one output. Here, each input (1, 2, 3) has exactly one output, so it is a function.

Step4: Count outputs for input 1

Input 1 has 1 output, which is 4.

Step5: Consider vertical - line test

If we graph this relation, since it is a function (each x - value has exactly one y - value), it would pass the vertical line test. A vertical line drawn through any x - value on the graph would intersect the graph at most once.

Answer:

1. {1, 2, 3}
2. {4, 5, 6}
3. Yes, because each input has exactly one output.
4. 1
5. Yes, because it is a function and each x - value has exactly one y - value.