Answer
a. neither
b. $-4x-2h+1$, $h\ne0$
Work Step by Step
a. From the given function $f(x)=-2x^2+x-5$, we have $f(-x)=-2(-x)^2+(-x)-5=-2x^2-x-5$. Since $f(-x)\ne f(x)$ and $f(-x)\ne -f(x)$, the function is neither even nor odd.
b. With $h\ne0$, we have $\frac{f(x+h)-f(x)}{h}=\frac{-2(x+h)^2+(x+h)-5-(-2x^2+x-5)}{h}=\frac{-4xh-2h^2+h}{h}=-4x-2h+1$
