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how do you know whether something is a vertical or horizontal stretch or shrink? how do you know if it's horizontal or vertical?

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An horizontal compression (or stretch) acts on the horizontal axis, which is related with variable x. Then, we have

Now, a vertical compression (or stretch) acts on the vertical axis, which is related with variable y (or f(x)). Then, we have

If we have the following expression:


g(x)=(1)/(3)x^2+2

the parent function is


f(x)=x^2

so, in order to get g(x) from f(x), we need a translation up 2 units and a vertical stretch by 1/3, that is,


f(x)\Rightarrow g(x)=(1)/(3)f(x)+2

how do you know whether something is a vertical or horizontal stretch or shrink? how-example-1
how do you know whether something is a vertical or horizontal stretch or shrink? how-example-2
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