Question

problems 3 - 4: determine whether each table could represent a function. explain your thinking.
3.

input	4	1	0	1	4
output	-2	-1	0	1	2

4.

input	-2	-1	0	1	2
output	4	1	0	1	4

following tables could represent a function?

Explanation:

Problem 3:

Step1: Recall function definition

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

Step2: Check input-output pairs

Input values: \(4, 1, 0, 1, 4\) (wait, looking at the table, let's list input - output:
Input: \(4\) → Output: \(-2\)
Input: \(1\) → Output: \(-1\)
Input: \(0\) → Output: \(0\)
Input: \(1\) → Output: \(1\)
Input: \(4\) → Output: \(2\)
Here, input \(1\) has two outputs (\(-1\) and \(1\)), input \(4\) has two outputs (\(-2\) and \(2\)). So it's not a function.

Problem 4:

Step1: Recall function definition

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

Step2: Check input - output pairs

Input values: \(-2, -1, 0, 1, 2\)
Input: \(-2\) → Output: \(4\)
Input: \(-1\) → Output: \(1\)
Input: \(0\) → Output: \(0\)
Input: \(1\) → Output: \(1\)
Input: \(2\) → Output: \(4\)
Each input has exactly one output. So it is a function.

Answer:

• Problem 3: The table does not represent a function because the input values \(1\) and \(4\) each have more than one output.
• Problem 4: The table represents a function because each input has exactly one output.