find the difference quotient for the function f(x)=9x + 8, and simplify it. the difference quotient is…

Explanation:

Step1: Recall the difference - quotient formula

The difference - quotient formula for a function $y = f(x)$ is $\frac{f(x + h)-f(x)}{h}$, where $h\neq0$. Given $f(x)=9x + 8$, then $f(x + h)=9(x + h)+8=9x+9h + 8$.

Step2: Substitute $f(x + h)$ and $f(x)$ into the formula

$\frac{f(x + h)-f(x)}{h}=\frac{(9x + 9h+8)-(9x + 8)}{h}$.

Step3: Simplify the numerator

$(9x + 9h+8)-(9x + 8)=9x+9h + 8 - 9x - 8=9h$.

Step4: Simplify the fraction

$\frac{9h}{h}=9$ (since $h\neq0$).

Answer:

$9$