Transformations applied in a different order can produce different functions. Follow a point through each step. Example Start with y=f(x). Stretch vertically by 3, then translate up by 2: y=3f(x)+2, with (u,v) to (u,3v+2). Translate up by 2, then stretch vertically by 3: y=3(f(x)+2)=3f(x)+6. For f(x)=x2, the resulting vertices are (0,2) and (0,6), respectively.

Transformations applied in a different order can produce different functions. Follow a point through each step.

Start with \(y=\mathrm{f}(x)\). Stretch vertically by \(3\), then translate up by \(2\): \(y=3\mathrm{f}(x)+2\), with \((u,v)\mapsto(u,3v+2)\).

Translate up by \(2\), then stretch vertically by \(3\): \(y=3(\mathrm{f}(x)+2)=3\mathrm{f}(x)+6\).

For \(\mathrm{f}(x)=x^2\), the resulting vertices are \((0,2)\) and \((0,6)\), respectively.

Transformations of Graphs

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Combining transformations

Combining transformations