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