1. The problem asks to find $f(-x)$ and $-f(-x)$ for the function $f(x)$, then compare these with $f(x)$ to determine if the function is even, odd, or neither. 2. Recall the definitions: - A function $f$ is even if $f(-x) = f(x)$ for all $x$. - A function $f$ is odd if $f(-x) = -f(x)$ for all $x$. - Otherwise, the function is neither even nor odd. 3. Let's analyze the first function: **a) $f(x) = x^2 - 4$** - Compute $f(-x) = (-x)^2 - 4 = x^2 - 4$ - Compute $-f(-x) = -(x^2 - 4) = -x^2 + 4$ - Compare: - $f(-x) = x^2 - 4 = f(x)$, so $f$ is even. Final answer: $f(x) = x^2 - 4$ is an even function.