Stretching graphs

Hi, guys can anyone help me with this please: if I’m stretching a graph, is the factor basically the reciprocal of the value you multiply by?

If I had the graph y = x^2 + 1
And stretched it to look like y = (2x)^2 + 1
The multiplier is 2 so the factor is 1/2

Is that accurate?

Yes.

If you change y=f(x) into y=f(ax) then this is horizontal stretch by scale factor 1/a.

If you change y=f(x) into by=f(x) [or] then this is a vertical stretch by scale factor 1/b.