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

Sagot :

AlgebraicAardvark

In general, the difference quotient is [tex]\dfrac{f(x+h)-f(x)}{h}[/tex].

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

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

and

    [tex]f(x) = -5x+8[/tex]

We'll plug that back into the difference quotient:

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

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