Math precalculus

Question

The graph of y = f(x) is transformed to the graph of y = f(-x). Which line(s) will the invariant points lie?

Answer 1

y=x transformed to y=-x has only the origin (0,0) as remaining the same. If (x,y) is on y=x then (x,-y) and (-x,y) are on the transformed equation.

y=x^2 "transformed" to y=(-x)^2 doesn't change at all, it's all the same curve or line

y=cosine(x) transformed to y=cos(-x) doesn't change either. It's still all the same curve

y=sin(x) transformed to y=sin(-x) leaves the points (npi, 0) the same, where n= any integer

y= absolute value of x transformed to y = absolute value of -x leaves all points the same, with the same lines that intersect at the origin.