If y = x^3 + 2x^2 if reflected across the line y =x, what is the resulting equation?
This is what I have so far:
x = y^3 - 2y^2
x = y^2 (y - 2)
x/(y-2) = y^2 <---- this is where my problem starts, I know I am not supposed to have y on both sides but am unsure as to how I eliminate it.
why the minus sign? Reflecting across y=x is just like finding the inverse function. In other words, you have
x = y^3+2y^2
see the graphs at
http://www.wolframalpha.com/input/?i=plot+y%3Dx%5E3+%2B+2x%5E2,+x%3Dy%5E3%2B2y%5E2,+y%3Dx
To reflect a function across the line y =x, you need to swap the x and y variables. The resulting equation will have x as the dependent variable and y as the independent variable.
Starting from your equation x/(y-2) = y^2, you can follow these steps to eliminate the y variable:
1. Multiply both sides of the equation by (y - 2) to get rid of the denominator:
x = y^2 * (y - 2)
2. Expand the right side of the equation:
x = y^3 - 2y^2
So, the resulting equation after reflecting the original equation across the line y =x is x = y^3 - 2y^2.