Question

identify whether the graph of the function $f(x)$ shown below is even, odd, or neither.

answer attempt 1 out of 3
the graph is because

Explanation:

Step1: Recall definitions

A function \( f(x) \) is even if \( f(-x) = f(x) \) (symmetric about \( y \)-axis), odd if \( f(-x) = -f(x) \) (symmetric about origin).

Step2: Analyze graph symmetry

Check the graph: For every point \( (x, y) \) on the graph, the point \( (-x, -y) \) should also be on it (origin symmetry). Visually, the left side is the mirror image of the right side across the origin. So \( f(-x) = -f(x) \).

Answer:

odd, it is symmetric about the origin (satisfies \( f(-x) = -f(x) \))