Requesting help on writing the formula of the transformation of the original function

[bestgio]

Hi everyone,
So I am trying to figure out what the transformation of the original function is. As you can tell, the left graph is the original function and the right graph is the transformation function. What I do know about the transformation is that there is a reflection across the x-axis. I drew the reflection of the original function across the x-axis just for reference. What I am having trouble with is figuring out what else happened to the transformation. I think it is a vertical stretch but how would I figure out how much is the transformation stretching by?

Any help is greatly appreciated!

 

[Deleted member 4993]

Hi everyone,
So I am trying to figure out what the transformation of the original function is. As you can tell, the left graph is the original function and the right graph is the transformation function. What I do know about the transformation is that there is a reflection across the x-axis. I drew the reflection of the original function across the x-axis just for reference. What I am having trouble with is figuring out what else happened to the transformation. I think it is a vertical stretch but how would I figure out how much is the transformation stretching by?

Any help is greatly appreciated!

The figures posted are too small and sketchy to ventut=re guesses regarding stretching.

 

[bestgio]

The figures posted are too small and sketchy to ventut=re guesses regarding stretching.

Weird
I'm able to see the full quality of the photo and still zoom into it after clicking the photo with the numbers still readable. Did I do something wrong?

 

[Ishuda]

Hi everyone,
So I am trying to figure out what the transformation of the original function is. As you can tell, the left graph is the original function and the right graph is the transformation function. What I do know about the transformation is that there is a reflection across the x-axis. I drew the reflection of the original function across the x-axis just for reference. What I am having trouble with is figuring out what else happened to the transformation. I think it is a vertical stretch but how would I figure out how much is the transformation stretching by?

Any help is greatly appreciated!

HINT: Can one infer anything else about the original function, y₁(x), from the graph? For example
y₁(x) = (x+2)² / 2; x \(\displaystyle \le\) -2
y₁(x) = (x+2) / 2; x \(\displaystyle \ge\) -2
or some such. If so, would that help any?

For example, consider (part of) the transformed function y₂(x) using the above,
y₂(x) = a y₂(x) + b; x \(\displaystyle \ge\) -2
Well, assuming I'm reading the graph correctly,
y₂(-2) = a y₂(-2) + b = 0 a + b = 3
y₂(4) = a y₂(4) + b = 3 a + b = -3
So solve for a and b. Now do the same thing to the other side.