Question

find the difference quotient $\frac{f(x + h)-f(x)}{h}$, $h
eq0$, for the given function $f$.
$f(x)=-9x + 2$
question help: written example
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Explanation:

Step1: Find $f(x + h)$

Substitute $x+h$ into $f(x)$:
$f(x + h)=-9(x + h)+2=-9x-9h + 2$

Step2: Calculate $f(x + h)-f(x)$

$f(x + h)-f(x)=(-9x-9h + 2)-(-9x + 2)$
$=-9x-9h + 2 + 9x-2=-9h$

Step3: Find the difference quotient

$\frac{f(x + h)-f(x)}{h}=\frac{-9h}{h}=-9$

Answer:

$-9$