Posted by **Anonymous** on Tuesday, February 9, 2010 at 9:24pm.

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.

- Math -
**engmath**, Tuesday, February 9, 2010 at 10:24pm
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

- Math -
**engmath**, Tuesday, February 9, 2010 at 10:35pm
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!

- Math -
**Anonymous**, Wednesday, February 10, 2010 at 8:13pm
recommended steps for factoring a polynomial

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