Question

input = 1: exactly one output, which is 2
input = 2: exactly one output, which is 1
input = 3: more than one output
input = 4: exactly one output, which is 3
decide if the graph shows a function by answering both questions.
does each input have exactly one output?
?
does the graph show a function?
?

Explanation:

Step1: Recall the definition of a function

A function is a relation where each input (x - value) has exactly one output (y - value).

Step2: Analyze the given inputs

• For input \( x = 1 \), output is \( 2 \) (one output).
• For input \( x = 2 \), output is \( 1 \) (one output).
• For input \( x = 3 \), there are more than one outputs (since there are two points with \( x = 3 \), \( y = 2 \) and \( y = 3 \)).
• For input \( x = 4 \), output is \( 3 \) (one output).

Step3: Answer the first question

Since the input \( x = 3 \) has more than one output, the answer to "Does each input have exactly one output?" is No.

Step4: Answer the second question

Since a function requires each input to have exactly one output, and here \( x = 3 \) has more than one output, the graph does not show a function. So the answer to "Does the graph show a function?" is No.

Answer:

For "Does each input have exactly one output?": No
For "Does the graph show a function?": No