17. given the following function, determine the difference quotient, $\frac{f(x + h)-f(x)}{h}$. $f(x)=-5x - 3$

Explanation:

Step1: Find $f(x + h)$

Substitute $x+h$ into $f(x)$: $f(x + h)=-5(x + h)-3=-5x-5h - 3$

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

$f(x + h)-f(x)=(-5x-5h - 3)-(-5x - 3)$ $=-5x-5h - 3 + 5x+3=-5h$

Step3: Find the difference quotient

$\frac{f(x + h)-f(x)}{h}=\frac{-5h}{h}$ Since $h\neq0$, we can cancel out $h$: $\frac{-5h}{h}=-5$

Answer:

$-5$