# Functional Transformation

• Oct 5th 2013, 07:04 AM
Functional Transformation
If \$\displaystyle F(x)= sqrt(x) \$, describe the transformation from \$\displaystyle F(x) \$to \$\displaystyle G(x)\$ if \$\displaystyle G(x) = -f(-x+1)-7 \$
• Oct 5th 2013, 07:14 AM
votan
Re: Functional Transformation
Quote:

If \$\displaystyle F(x)= sqrt(x) \$, describe the transformation from \$\displaystyle F(x) \$to \$\displaystyle G(x)\$ if \$\displaystyle G(x) = -f(-x+1)-7 \$

is f function the same as F function with different argument? if so, then G(x) = -sqrt(-x + 1) - 7 for x <= 1
• Oct 5th 2013, 08:01 AM
SlipEternal
Re: Functional Transformation
If, alternatively, you are looking for a description of the graph of the new function (i.e. shifts/rotations about lines/stretching/skewing/etc.), then break it down step-by-step.

Compare the graph of \$\displaystyle f(x)\$ to the graph of \$\displaystyle f(x-1)\$. Then compare those to the graph of \$\displaystyle f(-(x-1)) = f(-x+1)\$. Next, compare them to the graph of \$\displaystyle -f(-x+1)\$. Finally, put it all together as you compare it to the graph of \$\displaystyle -f(-x+1)-7\$.
• Oct 5th 2013, 06:42 PM
Re: Functional Transformation
Quote:

Originally Posted by SlipEternal
If, alternatively, you are looking for a description of the graph of the new function (i.e. shifts/rotations about lines/stretching/skewing/etc.), then break it down step-by-step.

Compare the graph of \$\displaystyle f(x)\$ to the graph of \$\displaystyle f(x-1)\$. Then compare those to the graph of \$\displaystyle f(-(x-1)) = f(-x+1)\$. Next, compare them to the graph of \$\displaystyle -f(-x+1)\$. Finally, put it all together as you compare it to the graph of \$\displaystyle -f(-x+1)-7\$.

Yes, I have no idea how to break it down, but this is what I'm looking for.
• Oct 6th 2013, 07:00 AM