Find a function whose graph is the given curve.

Question

the bottom half of the circle: x²+y²=81

f(x)=_________

Answer 1

x²+y²=81 is a whole circle with a radius of 9. If we solve for y², we get:

y² = 81 - x²

To solve for y, we need to take the square root of both sides. Remember though, a square root has 2 answers, positive and negative.

y = ± √(81 - x²)

The positive part is the top half of the circle, the negative part is the bottom half. Therefore our answer is:

y = -√(81 - x²)

Answer 2

f(x) = -√81 - x²)