Question

is the function v(x) even, odd, or neither? even odd neither

Explanation:

Step1: Recall symmetry rules

A function is even if its graph is symmetric about the y - axis, i.e., \(v(-x)=v(x)\) for all \(x\) in the domain. A function is odd if its graph is symmetric about the origin, i.e., \(v(-x)= - v(x)\) for all \(x\) in the domain.

Step2: Analyze the graph

Looking at the graph of \(v(x)\), we check for symmetry. The graph appears to be symmetric about the y - axis. For example, the part of the graph to the left of the y - axis (negative x - values) is a mirror image of the part to the right of the y - axis (positive x - values). This satisfies the condition for an even function (\(v(-x) = v(x)\)).

Answer:

even