find the difference quotient and simplify. f(x)=-8x + 9 the difference quotient of f(x) is

Explanation:

Step1: Recall difference - quotient formula

The difference - quotient formula is $\frac{f(x + h)-f(x)}{h}$, where $h\neq0$. Given $f(x)=-8x + 9$, first find $f(x + h)$. $f(x + h)=-8(x + h)+9=-8x-8h + 9$.

Step2: Substitute into difference - quotient formula

Substitute $f(x + h)$ and $f(x)$ into $\frac{f(x + h)-f(x)}{h}$: [ \begin{align*} \frac{f(x + h)-f(x)}{h}&=\frac{(-8x-8h + 9)-(-8x + 9)}{h}\ &=\frac{-8x-8h + 9 + 8x-9}{h} \end{align*} ]

Step3: Simplify the expression

Combine like - terms in the numerator: $(-8x+8x)+(-8h)+(9 - 9)=-8h$. So, $\frac{-8h}{h}=-8$.

Answer:

$-8$