Question

1. is each relation a function? if so, is it one - to - one or not one - to - one?

a.
b.

Explanation:

Step1: Analyze part a (function check)

Each input has exactly one output: $-2 \to 5$, $3 \to 6$, $3 \to 7$ is invalid? No, wait: $-2$ maps to 5, $3$ maps to 6 and 7, $4$ maps to 8. A function requires each input to have only one output. Since input 3 has two outputs, this is not a function.

Step2: Analyze part b (function check)

Use vertical line test: any vertical line intersects the graph at most once. This linear graph passes the test, so it is a function.

Step3: Analyze part b (one-to-one check)

Use horizontal line test: any horizontal line intersects the graph at most once. This linear graph (non-horizontal) passes the test, so it is one-to-one.

Answer:

a. This relation is not a function (input 3 maps to two different outputs).
b. This relation is a one-to-one function (passes both vertical and horizontal line tests).