Question

use the graph to determine whether the function is even, odd, or neither.

Explanation:

Step1: Recall even function graph rule

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

Step2: Analyze the given graph

Observe the graph: for any positive $x$-value, the point $(-x, y)$ has the same $y$-value as $(x, y)$. The graph is a mirror image across the $y$-axis, which matches the symmetry requirement for an even function.

Step3: Rule out odd function

An odd function is symmetric about the origin (for every $(x,y)$, $(-x,-y)$ exists), which does not match this graph.

Answer:

The function is even.