1. ## Function Transformations

ok, I know this is a basic, but I have completely forgot

If f(x)= x^2 - 1, describe in words what the following would do to the graph of f(x):

abs(f(x))

and also, they've drawn a graph with cordinates and they tell you to transform it so that y=f(abs(x))

2. Can you answer the question from this graph?

3. but is abs(f(x)) different than f(abs(x)) cause the worksheet seems to think so

also, how would one describe that in words?? lol ...

4. This is a differrent function. Study it.
Can you see what is going on?

5. wait, ok, so it shifts everything up so its positive
but whats the difference in the absolute value of the entire f(x) verses f(abs(x))?

so if you had a figure with cordinates like (-4, 0) (0,2) (1,0) (2,-2) (3,0)
and you wanted to make it f(abs(x)) and also abs(f(x)) how would you do that? would you make that dropped down V positive and disconnect the lines and points?

wait, ok, I get the f(abs(x)) (make the negative reflect off of axis)
but the abs(f(x)), how is that different?

6. Originally Posted by cassiopeia1289
whats the difference in the absolute value of the entire f(x) verses f(abs(x))?
Think of the y-axis as a miror. It just copies the positive x-side.

7. could you possible just give me the answer, I'm one of those people that goes backwards and teaches myself, that's the way I run, weird I know, but I just need the difference between the two and then I'll try and figure it
but the figure I need is more like a star connection, ya know? its not the swoopy line, I get those, but its lines connected by dots

8. ok, I take it back, could you sketch a connected dot figure just plainly, then do y=f|x| to the graph and then seperately do y=|f(x)|
also, how do you know which side to reflex?

9. I take all of it back, |f(x)| makes everything have to be positive so it flips and f|(x)| is the mirror one, right???

10. Now that you have done some work (thought) on your own, I can help you more.
Once we have a graph of $\displaystyle f(x)$ then because $\displaystyle \left| x \right| \ge 0$ then the whole graph of $\displaystyle f\left( {\left| x \right|} \right)$ just looks like the right-hand (the positive side of the y-axis, the first and fourth quadrants).

Example: for every x it is true that $\displaystyle f\left( {\left| x \right|} \right) = f\left( {\left| { - x} \right|} \right)$.

So just copy the right-hand of the graph to the left-hand letting the y-axis act as a mirror.