Question

value: 3
identify if the graph is even, odd, or neither.
graph with x-axis from -10 to 10 and y-axis from -10 to 10, showing a v - shaped graph with vertex at (0, - 3), left arm going from (0, - 3) to (-10, 9) and right arm going from (0, - 3) to (10, 9)

Explanation:

Step1: Recall even function test

A function's graph is even if it is symmetric about the $y$-axis. This means for every point $(x,y)$ on the graph, $(-x,y)$ is also on the graph.

Step2: Recall odd function test

A function's graph is odd if it is symmetric about the origin. This means for every point $(x,y)$ on the graph, $(-x,-y)$ is also on the graph.

Step3: Check symmetry of given graph

Observe the graph: for a point like $(2,0)$, $(-2,0)$ exists; for $(4,2)$, $(-4,2)$ exists. The graph is a mirror image across the $y$-axis, satisfying the even function symmetry rule, and does not satisfy the origin symmetry for odd functions.

Answer:

Even