SOLUTION: Can you explain why y=x^2 is the graph of a function of x, while x=y^2 is not the graph of a function of x?

Algebra ->  Functions -> SOLUTION: Can you explain why y=x^2 is the graph of a function of x, while x=y^2 is not the graph of a function of x?      Log On


   

Question 238636: Can you explain why y=x^2 is the graph of a function of x, while x=y^2 is not the graph of a function of x?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In order to be a function, each x must match with a single
f%28x%29. In the 1st case, f%28x%29+=+x%5E2, and there can only be
one x for each f%28x%29.
In the 2nd case, +f%28x%29+=+%2B+sqrt%28x%29, and f%28x%29+=+-sqrt%28x%29
Each x matches with 2 values of f%28x%29
Here's a graph of each. The curve on the right is not a function
+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2C+sqrt%28x%29%2C+-sqrt%28x%29%29+