# Thread: How do you do the transformation for these functions?

1. ## How do you do the transformation for these functions?

Hello,
First graph is y=f(x) with the points (-4,1),(-2,1),(0,-1) and (1,0)

Then f(x) is transformed by the equation y=2|f(x)|-1

I understand how to do the vertical stretches and the translations. However, how will the absolute value of the function come into play? Do I first change all the negative y values to positive like (0,-1) would be (0,1)?

Also, how would the original f(x) graph be transformed with this equation y=|2f(x)-1|. Would the -1 in the equation be a vertical translation of +1 because its absolute value?

Could I get the final points
of the transformed graph for each equation? Thanks!

2. ## Re: How do you do the transformation for these functions?

don't make this more difficult than it isn't ...

$(x,f(x)) = \{(-4,1),(-2,1),(0,-1),(1,0)\}$

$(x,2|f(x)|-1) = \{(-4,1),(-2,1),(0,1),(1,-1)\}$

$(x,|2f(x)-1|) = \{(-4,1),(-2,1),(0,3),(1,1)\}$

3. ## Re: How do you do the transformation for these functions?

Originally Posted by Latinized
[FONT="]Hello,
First graph is y=f(x) with the points (-4,1),(-2,1),(0,-1) and (1,0) [/FONT]

[FONT="]Then f(x) is transformed by the equation y=2|f(x)|-1 [/FONT]

[FONT="]I understand how to do the vertical stretches and the translations. However, how will the absolute value of the function come into play? Do I first change all the negative y values to positive like (0,-1) would be (0,1)? [/FONT]

[FONT="]Also, how would the original f(x) graph be transformed with this equation y=|2f(x)-1|. Would the -1 in the equation be a vertical translation of +1 because its absolute value?

Could I get the final points [/FONT]
of the transformed graph for each equation? Thanks!
Come on. You've go to do some of the work, but I'll get you started.

Take the first point (-4, 1) and the first transformation y=2|f(x)|-1
The point (-4, 1) is another way of saying f(-4)=1
So:
y=2|f(x)|-1
y=2|f(-4)|-1
y=2|1|-1
y=2*1-1
y=1.................so (-4, 1) transforms onto (-4, 1) itself

Now ake the first point (-4, 1) and the second transformation y=|2f(x)-1|.
The point (-4, 1) is another way of saying f(-4)=1
So
y=|2f(x)-1|
y=|2f(-4)-1|
y=|2*1-1|
y=1 ......so (-4, 1) transforms on to (-4, 1) again ...this won't always happen!

Now try the other points for yourself.

4. ## Re: How do you do the transformation for these functions?

I get the same answers for the first equation, however I don't do it the way you guys do it. I vertically stretch it, translate it, etc... on the graph.

The second equation,y=|2f(x)-1|, I don't get the same answer. Since the b value is 2, doesn't it mean that the graph is being horizontally compressed by a factor of 1/2?

As a result, all the x values have to be multiplied by 0.5. Then, the y values will change as it's translated by -1. Thus, the answer I get is (-2,0), (-1,0), (0,0) and (0.5,-1)

5. ## Re: How do you do the transformation for these functions?

The second equation,y=|2f(x)-1|, I don't get the same answer. Since the b value is 2, doesn't it mean that the graph is being horizontally compressed by a factor of 1/2?
no, you're confusing $2f(x)$ with $f(2x)$ ... $f(2x)$ compresses the graph horizontally.

taking the transformations one-by-one ...

$y = |f(x)|$ reflects all negative y-values over the x-axis

$y = |2f(x)|$ doubles all y-values and then reflects all the negative doubled y-values over the x-axis

$y = |2f(x) - 1|$ double all y-values, subtracts 1, and then reflects all the (doubled - 1) negative y-values over the x-axis