Answer
$a)$ $f(x+h)=-4x-4h+2$
$b)$ $f(x+h)-f(x)=-4h$
$c)$ $\frac{f(x+h)-f(x)}{h}=-4$
Work Step by Step
$a)$
$$f(x)=-4x+2$$
Replace $x$ with $x+h$:
$$f(x+h)=-4(x+h)+2$$
$$f(x+h)=-4x-4h+2$$
$b)$
$$f(x+h)-f(x)$$
Substitute corresponding expressions:
$$-4x-4h+2-(-4x+2)$$
$$-4x-4h+2+4x-2=-4h$$
$c)$
$$\frac{f(x+h)-f(x)}{h}$$
Substitute corresponding expression for numerator:
$$\frac{-4h}{h}=-4$$
