Being able to transform basic graphs is an essential skill to develop for sketching graphs.
Here I look at stretches to graphs of the form y = f(x).

Transformations of Graphs (stretches) : ExamSolutions - youtube Video

Why does y = af(x) stretch y = f(x) by scale factor a parallel to the y-axis?

Transformations of Graphs (stretches 1) Proof : ExamSolutions - youtube Video

Why does y = f(ax) stretch y = f(x) by scale factor 1/a parallel to the x-axis?

Transformations of Graphs (stretches 2) Proof : ExamSolutions - youtube Video