Question

relationships mini retest

1. which mapping represents y as a function of x?

Explanation:

Step1: Recall function definition

A relation is a function if for each input \(x\) there is exactly one output \(y\).

Step2: Analyze first mapping

In the first mapping with \(x = \{0.25,0.35,0.45,0.55\}\) and \(y=\{0.50,0.70,0.90,1.10\}\), each \(x\) - value is mapped to exactly one \(y\) - value.

Step3: Analyze second mapping

In the second mapping with \(x = \{20,40,60,80\}\) and \(y = \{5,10,15,20\}\), the value \(x = 40\) is mapped to both \(y = 10\) and \(y = 15\), so it is not a function.

Step4: Analyze third mapping

In the third mapping with \(x=\{0,4\}\) and \(y=\{- 5,-9,-13\}\), the value \(x = 0\) is mapped to both \(y=-5\) and \(y = - 9\), so it is not a function.

Answer:

The first mapping (with \(x = \{0.25,0.35,0.45,0.55\}\) and \(y=\{0.50,0.70,0.90,1.10\}\)) represents \(y\) as a function of \(x\).