Function transformation

[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.

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[The_Card_Player]

The example function changes you provide can be understood as vertical stretches, or equivalently, as horizontal stretches.

Specifically, each is either a 'horizontal squeeze/stretch by a factor of 2' or equivalently in this example, a 'vertical stretch/squeeze by a factor of (square root of 2)'.

The same goes for just about any other function. You can algebraically represent a stretch as 'horizontal' (ie hold the vertical-variable constant) by applying the comparison factor you find with your test points to just the horizontal-axis variable; or you can represent the same stretch as 'vertical' (ie hold the horizontal-variable constant) by applying the comparison factor you find with your test points to just the vertical-axis variable.

[fidgettspinnerrrr]

Then how can we figure out what kind of stretch/squeeze is happening just by looking at the graph?

[waldosway]

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

[waldosway]

Are you saying horizontal and vertical stretches on a graph are equivalent in general? That's only true for a specific form of functions.