Find the difference quotient of $LaTeX: \displaystyle f(x)=x - 8$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=h + x - 8$ and expanding gives $LaTeX: \displaystyle f(x+h)=h + x - 8$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(h + x - 8)-(x - 8)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{h}{h}=1$