Question

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

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

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

Answer:

-1