Question

look at this graph:
is this relation a function?

Explanation:

Step1: Recall function definition

A relation is a function if each input (x-value) has exactly one output (y-value). We use the vertical line test: any vertical line intersects the graph at most once.

Step2: List all x-values

Identify x-coordinates of points: $x=-4, x=-3, x=-2, x=-2, x=-1, x=2$

Step3: Check for repeated x-values

The x-value $x=-2$ appears twice, with different y-values. This fails the vertical line test.

Answer:

No, this relation is not a function.