Question

look at this graph: is this relation a function? yes no

Explanation:

A relation is a function if every input (x-value) has exactly one output (y-value). Check each x-coordinate of the points:

• $x=-5$: $y=6$ (one y-value)
• $x=-2$: $y=-4$ (one y-value)
• $x=1$: $y=6$ and $y=-4$ (two y-values for one x-value)

Since one x-value maps to two different y-values, the relation fails the vertical line test (a vertical line through $x=1$ would intersect two points), so it is not a function.

Answer:

no