Whenever graphing a circle via a transformation of y=f(x), will it always be a half circle/ellipse or is it possible for that y=f(x) transformation to contain both halves?
For example, in this case,
f(x)=sqrt(1-x^2)
if i were to write a transformation of this as
y=3*f(x/2)-9, would this be a half ellipse since it contains that f(x)? if so, would adding a ± before the 3 make it a full ellipse or would that just not work since its still f(x)?
