Can you stretch a function with a zero or undefined gradient?

Question

If $y=f(x)$ is either $y=3$ (zero gradient) or $x=2$ (undefined gradient), is it possible to stretch $y=f(x)$ by graphing $y=af(x)$ or $y=f(ax)$? If it is possible to stretch them, can you only stretch them parallel to one of the axes or both?

Answer 1

Note that the equations you mention don't describe a function, but they do describe a set of points in the plane.

It is always permissible to replace $y$ by $y/a$ or $x$ by $x/b$ (for nonzero $a$ and $b$) in the defining equations to produce vertical or horizontal scaling of the point set, with the caveat that any limitations on $x$ or $y$ in the original set of equations may need to be adjusted appropriately.