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?

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.

Sure! I'd be happy to help break down each step of the transformations for the given relation.

The original relation is: x^2 + 3x = y^2 - 2y.

A. Vertical expansion by 2:
To vertically expand a relation by a factor of 2, we need to multiply the right side of the equation by 2. So the new relation becomes: x^2 + 3x = 2(y^2 - 2y).

B. Horizontal expansion by 3:
To horizontally expand a relation by a factor of 3, we need to divide the x values by 3. So the new relation becomes: (x/3)^2 + 3(x/3) = y^2 - 2y.

C. Vertical compression by 4/5:
To vertically compress a relation by a factor of 4/5, we need to multiply the right side of the equation by 4/5. So the new relation becomes: x^2 + 3x = (4/5)(y^2 - 2y).

D. Horizontal compression by 1/5:
To horizontally compress a relation by a factor of 1/5, we need to multiply the x values by 1/5. So the new relation becomes: ((1/5)x)^2 + 3((1/5)x) = y^2 - 2y.

E. Reflection over y-axis, vertical expansion by 5, and horizontal expansion by 9:
First, let's reflect the relation over the y-axis. To do this, we change the signs of the x terms, which gives us: (-x)^2 + 3(-x) = y^2 - 2y.

Next, we vertically expand the relation by 5. We multiply the right side of the equation by 5, resulting in: (-x)^2 + 3(-x) = 5(y^2 - 2y).

Finally, we horizontally expand the relation by 9. We divide the x values by 9, leading to: ((-x)/9)^2 + 3((-x)/9) = 5(y^2 - 2y).

These are the new relations obtained after each transformation. I hope this helps clarify the steps! Let me know if you have any further questions.