SOLUTION: Problem: Determine whether the equation defines y as a function of x. Explain why or why not. a.) x^2+y=9 b.) x+sqrt(y)=5

Algebra ->  Functions -> SOLUTION: Problem: Determine whether the equation defines y as a function of x. Explain why or why not. a.) x^2+y=9 b.) x+sqrt(y)=5       Log On


   

Question 947367: Problem: Determine whether the equation defines y as a function of x. Explain why or why not.
a.) x^2+y=9

b.) x+sqrt(y)=5
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Yes to both.

#1 is obvious because you solve for y in terms of x.

#2, less obvious.
x%2Bsqrt%28y%29=5, one branch of a parabola.
sqrt%28y%29=-x%2B5, and you must have y%3E=0.
square both sides.
y=%285-x%29%5E2, .

The part for which y is non-negative would be the actual graph.
graph%28300%2C300%2C-8%2C12%2C-8%2C12%2C%285-x%29%5E2%29


Also multiply the right member.
y=25-10x%2Bx%5E2
y=x%5E2-10x%2B25
and that is the same as y=%28x-5%29%5E2.