Transforming graphs: why is transforming x^2 to 1/2x^2 called a vertical compression?

[tonimaroni]

So why is transforming x^2 to 1/2x^2 called a vertical compression if when you put the graphs in on your calculator 1/2x^2 is a stretch not a compression?? (I thought a vertical compression was anything between 0 and 1 so it makes sense that 1/2 would be a compression but then why does it show up stretched?

 

[tkhunny]

Do you have the same SCALE for each graph?

It is possible that a stretch can look like a vertical compression. The proof is in the development.

\(\displaystyle \dfrac{1}{2}x^{2} = \left(\dfrac{x}{\sqrt{2}}\right)^{2}\)

The one on the left is a vertical compression.
The one on the right is this stretch you are seeing.

Some functions, and some variations, can have more than one way to get there.

 

[mmm4444bot]

So why is transforming x^2 to 1/2x^2 called a vertical compression if when you put the graphs in on your calculator 1/2x^2 is a stretch not a compression?

It is because that stretch you're seeing is a horizontal stretch.

A horizontal stretch is a vertical compression.

A horizontal compression is a vertical stretch. :cool: