SOLUTION: The graph of the relation y-x^2 = 1/2x+y is stretched vertically by a factor of 4 and stretched horizontally by a factor of 7. Give the equation of the relation described by this n

Algebra ->  Rational-functions -> SOLUTION: The graph of the relation y-x^2 = 1/2x+y is stretched vertically by a factor of 4 and stretched horizontally by a factor of 7. Give the equation of the relation described by this n      Log On


   

Question 52346: The graph of the relation y-x^2 = 1/2x+y is stretched vertically by a factor of 4 and stretched horizontally by a factor of 7. Give the equation of the relation described by this new geaph
Answer by ChillyWiz(11) About Me  (Show Source):
You can put this solution on YOUR website!
Think... when an equation is "stretched", what happens?
To stretch a whole function by a factor of 4 vertically, f(x) -> 4*f(x)
To stretch a whole function by a factor of 7 horizontally, f(x) -> f(x/7)
But since this is an relation, lets solve for x instead of y
y-x%5E2+=+%281%2F2%29x+%2B+y
-x%5E2+=+%281%2F2%29x
x+=+-2x%5E2
2x%5E2%2Bx=0
x%282x%2B1%29=0
This is basically the graph of two vertical linesx=0 x=-%281%2F2%29
a vertical line stretched 4 times vertically will still be the same
a vertical line stretched 7 times horizontally will still be the same
The stretched relation will still be the same as the original equation.