Question

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

Explanation:

Step1: Recall definitions

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

Step2: Analyze graph symmetry

The graph of \( c(x) \) is symmetric about the \( y \)-axis (left and right of \( y \)-axis mirror each other). For example, the point \( (2, y) \) and \( (-2, y) \) have the same \( y \)-value. So \( c(-x)=c(x) \).

Answer:

even