Determine whether the equation defines y as a function of x

Determine whether the equation defines y as a function of x. (See Example 9.) x^2 + (y - 7)^2 - 8 is a function is not a function Determine whether the equation defines y as a function of x. (See Example 9.) x^2y + y = 8 Is a function is not a function Determine whether the equation defines y as a function of x. (See Example 9.) is a function is not a function

Solution

For y as a function of x, for every x value there is no more than one y value

5) x^2 + (y - 7)^2 = 8 ======> (y - 7)^2 = 8 - x^2 ========> y = 7 ± (8 - x^2)

Here y has two values for every x. A function cannot assign more than one y to any x value. So not a function.

6) x^2y + y = 8 =====> y(x^2 + 1) = 8 =======> y = 8/(x^2 + 1) ======> Function

7) x = y^3 ====> y = x^(1/3) =====> Not function