# Functional Transformation

• Oct 5th 2013, 08:04 AM
Functional Transformation
If $F(x)= sqrt(x)$, describe the transformation from $F(x)$to $G(x)$ if $G(x) = -f(-x+1)-7$
• Oct 5th 2013, 08:14 AM
votan
Re: Functional Transformation
Quote:

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

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, 09:01 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 $f(x)$ to the graph of $f(x-1)$. Then compare those to the graph of $f(-(x-1)) = f(-x+1)$. Next, compare them to the graph of $-f(-x+1)$. Finally, put it all together as you compare it to the graph of $-f(-x+1)-7$.
• Oct 5th 2013, 07:42 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 $f(x)$ to the graph of $f(x-1)$. Then compare those to the graph of $f(-(x-1)) = f(-x+1)$. Next, compare them to the graph of $-f(-x+1)$. Finally, put it all together as you compare it to the graph of $-f(-x+1)-7$.

Yes, I have no idea how to break it down, but this is what I'm looking for.
• Oct 6th 2013, 08:00 AM
Let's consider what happens when we plug in numbers. If we plug in 5 to $f(x-1)$, we get $f(5-1) = f(4)$. Going from the graph of $f(x)$ to the graph of $f(x-1)$, the x-position of $f(4)$ is going from x=4 to x=5. In other words, it is shifting to the right one unit. Now let's consider $f(-(x-1))$. Now, $f(-4)$ is at x=-4 in our original graph, but it is at x=5 in this graph. Does this mean it is shifting to the right nine units? Not quite. Let's look at some more data to see what's happening. $f(-3)$ is the y-value at x=-3 in our original graph, but it is the y-value at x=4 in $f(-(x-1))$. So now the shift is only 7 units. The negative sign is actually creating a reflection across some axis. The closer we get to $x=1$, the less the points need to shift from the original function to our new function. In other words, this is a reflection across the line x=1. Next, $-f(-x+1)$ is taking the value $f(-x+1)$ and taking its reflection across the x-axis. Finally, $-f(-x+1)-7$ is taking the graph of $-f(-x+1)$ and shifting it down seven units.