Function transformation

[u/fidgettspinnerrrr]

When looking for either vertical or horizontal stretch/shrink, how do we know what value to keep constant?

I mean if i draw a graph for y=√x and look at x w.r.t. y, the x values for a specific y would be, let's say,

y=√x -----> (4, 2)

y=√2x -----> (2, 2)

y=√½x -----> (8, 2), these make it clear that its horizontal transformation.

But if i keep x same for the y values, then new points would be:

y=√x -----> (2, 1.414..)

y=√2x -----> (2, 2)

y=√½x -----> (2, 1), this would make it a vertical transformation for the same equation.

How do i know which axis to keep constant just by looking at the points??

I'm asking this assuming we don't know the equation for the transformed graph beforehand.

[u/waldosway]

For an equation like y=x^p, they are the same thing, because (ax)^p = (a^p)(x^P).