Question

Need help with this question, don't get it.

Given the relation x^2+3x=y^2-2y, what is the new relation if it has undergone:

A. vertical expansion by 2
B. Horizontal expansion by 3
C. Vertical compression by 4/5
D. Horizontal compression by 1/5
E. Reflection over yaxis, vertical expansion by 5 and a horizontal expansion by 9

I only get the basic stuff like:

Given the function y=f(x) what transformation occurs if

A. y is replaced with 2y. I get that, that would be a vertical compression by 1/2. But the question above I just don't get it, could someone please explain and simplify every step so I can understand?

Answer 1

If you understand that replacing y with 2y represents a compression by 1/2, the questions above should pose no problems.

A vertical expansion of 2 is achieved by replacing y by y/2. So,

x^2 + 3x = (y/2)^2 - 2(y/2)
x^2 + 3x = 1/4 y^2 - y

similarly for the others.

for (E), a reflection about y-axis is just a scaling x by -1. So, reflection and scaling is done by replacing x by -x/9.