Question

For the given functions, write the rational function,

r(x) = [f(x-h)-f(x)]/h and simplify:

a. F(x) = 2x+3
b. F(x) = 1/(x+1)
c. F(x) = x^2

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Just need to know that the rational function is and maybe I can do the questions. Thanks.

Answer 1

the rational function is r(x)=[f(x-h)-f(x)]/h (also known as the limit definition)
so if your function is F(x)=2x+3 plug it into the rational function
[2(x-h)+3-(2x+3)]/h
=[2x+2hx-3-2x-3]/h --->then simplify
=2h/h--->cancel the h's
=2
then do the same thing for the other problems

Answer 2

ah sorry... I was looking at your problem and thinking of something else. Here is the correct solution for part a
so therefore...
SO if F(x)=2x+3 plug it into your rational function r(x)=[f(x-h)-f(x)]/h
=[2(x-h)+3-(2x+3)]/h
=[2x-2h+3-2x-3]/h --->then simplify (cancel the 2x's and the 3's)
=-2h/h--->cancel the h's
=-2

Sorry about that screw-up. Hope you understand!

Answer 3

recommended steps for factoring a polynomial