Difference Quotient?

Question

Find the difference quotient for the function ​f(x)=−2x+7​, and simplify it.

Answer 1

The best way to go about this is by breaking it apart.

Difference Quotient Formula = [ f(x+h) - f(x) ] / h

f(x) = -2x + 7

f(x+h): -2(x+h) + 7 → -2x - 2h + 7

f(x+h) - f(x) = (-2x - 2h + 7) - (-2x + 7)

-2x - 2h + 7 + 2x - 7

The -2x and 2x cancel out, along with the 7 and -7

[ f(x+h) - f(x) ] / h = -2h/h = -2

The difference quotient for the function f(x) = -2x + 7 is [(-2x - 2h + 7) - (-2x + 7)] / h, which simplifies down to -2.