Question

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)?

Answer 1

it would be -3i and 3i of and not half (half circle as factoring -9 would be -6 /2 =-3 = 3 sq rt f(x) -3 = x/2 where x stays 1 sqrt of 1 * 3 -3 = 0 and here is a low line ascending curve see photo

Explanation:

Note that any positive real number has two square roots, one positive and one negative. For example, the square roots of 9 are -3 and +3, since (-3) 2 = (+3) 2 = 9. Any nonnegative real number x has a unique nonnegative square root r; this is called the principal square root The 2nd root of 9, or 9 radical 2, or the square root of 9 is written as -3

Answer 2

here to help!!

Explanation:

by J Orloff · Cited by 3 — We have shown that a line or circle in x, y is transformed to a line or circle in u, v. This shows that inversion maps lines and circles to lines and circles