###### Order of Transformations

Suppose that \(f(x)\) is our function we are applying transformations to. Once written in the form

the order of transformations is:

- horizontal stretch or compress by a factor of \(\abs{b}\) or \(\abs{\dfrac{1}{b}}\) (if \(b\lt 0\) then also reflect about \(y\)-axis)
- shift horizontally left/ right by \(\abs{h} \)
- vertically stretch or compress by a factor of \(\abs{a}\) or \(\abs{\dfrac{1}{a}}\) (if \(a\lt 0\) then also reflect about \(x\)-axis)
- shift vertically up/ down by \(\abs{k} \)