SOLUTION: Assume that all variables represent real numbers. Determine whether the equation determines y to be a function of x. y2 − 8x = 1 y is a function of x. y is not a function of

Algebra ->  Functions -> SOLUTION: Assume that all variables represent real numbers. Determine whether the equation determines y to be a function of x. y2 − 8x = 1 y is a function of x. y is not a function of      Log On


   

Question 1151550: Assume that all variables represent real numbers. Determine whether the equation determines y to be a function of x.
y2 − 8x = 1
y is a function of x.
y is not a function of x.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Determine whether the equation determines y to be a function of x.
y%5E2+-8x+=+1
y%5E2++=+8x%2B1
y+=+sqrt%288x%2B1%29
=> y+=+sqrt%288x%2B1%29 or y+=+-sqrt%288x%2B1%29
=>answer: it does not define y as a function of x, because some value(s) of x have more than one+y
proof:
we know 8x%2B1%3C%3E+0
and it will be if x=+-1%2F8
So, all the values of x larger than -1%2F8 would have two y values.
For example, if x=10 would be paired with y+=+sqrt%288%2A10%2B1%29=sqrt%2881%29=9 and y+=+sqrt%288%2A10%2B1%29=sqrt%2881%29=9
A function cannot assign more than one y to any x value.