Question

F(x) = -5x + 8
evaluate and simplify the difference quotient.

Answer 1

In general, the difference quotient is
`(f(x+h)-f(x))/(h)`.

Before we evaluate all of that, we need to find the two top pieces individually.

`\begin{aligned}\\f(x+h) &= -5(x+h)+8 \\[0.5em]&= -5x-5h+8\\\end{aligned}`

and

`f(x) = -5x+8`

We'll plug that back into the difference quotient:

`\begin{aligned}(f(x+h)-f(x))/(h) &= ((-5x-5h+8)-(-5x+8))/(h)\\[0.7em]&= (-5x-5h+8+5x-8)/(h)\end{aligned}`

Can you take it from there?