given the following function, determine the difference quotient, $\frac{f(x + h)-f(x)}{h}$. $f(x)=-x - 7$

Answer:

-1

Explanation:

Step1: Find (f(x + h))

Substitute (x+h) into (f(x)): (f(x + h)=-(x + h)-7=-x - h-7)

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

(f(x + h)-f(x)=(-x - h - 7)-(-x - 7)) (=-x - h - 7 + x+7=-h)

Step3: Calculate the difference - quotient

(\frac{f(x + h)-f(x)}{h}=\frac{-h}{h}=-1)