Question

Hey guys. I need help on pre-cal. I don't really understand horizontal and vertical stretches besides the fact that "a stretch by a factor of c if c > 1" and "a shrink by a factor of c if c < 1" I will post the question below.

Answer 1

Whenever you `multiply y by something`, it corresponds to a `vertical stretch`.
Whenever you `multiply x by something`, it corresponds to a `horizontal stretch`.

Answer 2

Think of f(x) as y.

Answer 3

\[\large\rm \color{orangered}{y=\sqrt x}\]We achieve our new function multiplying both sides by 8,\[\large\rm 8\color{orangered}{y}=8\color{orangered}{\sqrt x}\]
If f(x) = y
Then g(x) = 8y

This is a `vertical stretch` of f(x) by a factor of 8.
We manipulated the y.

Answer 4

It might be confusing the way I said that you're `multiplying y by something`.
But remember that this \(\large\rm \sqrt{x}\) is y.
So when you multiply that by 8, you're multiplying y by 8, because that is y.

Answer 5

To make horizontal stretches, you multiply x by a value.
Example:\[\large\rm f(x)=\sqrt{x}\qquad\to\qquad g(x)=\sqrt{4x}\]g(x) represents a `horizontal stretch` of f(x) by a factor of 4.

Answer 6

Thank you so much! No, I understood you completely it was much easier understanding your explanation than the textbook's. Thank you. :)

Answer 7

yay \c:/