SOLUTION: Given that f(x)=-3x+7 Find (f+h)-f(x)/h

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Question 1192924: Given that f(x)=-3x+7
Find (f+h)-f(x)/h
Found 2 solutions by math_tutor2020, josgarithmetic:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Replace every x with x+h
f%28x%29=-3x%2B7

f%28x%2Bh%29=-3%28x%2Bh%29%2B7

f%28x%2Bh%29=-3x-3h%2B7

Then compute the difference quotient.
%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+%28%28-3x-3h%2B7%29-%28-3x%2B7%29%29%2Fh

%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+%28-3x-3h%2B7%2B3x-7%29%2Fh

%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+%28-3h%29%2Fh

%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+-3
The idea is that h does not equal zero, but it gets closer and closer to it.
This is where the concept of limits come in.

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
This is just a matter of substitution and simplification.
Your quotient is supposed to be as %28f%28x%2Bh%29-f%28x%29%29%2Fh.