determine whether the following equation defines y as a function of x. x² + y = 1 does the equation x² + y =…

determine whether the following equation defines y as a function of x. x² + y = 1 does the equation x² + y = 1 define y as a function of x? yes no

determine whether the following equation defines y as a function of x. x² + y = 1 does the equation x² + y = 1 define y as a function of x? yes no

Answer

Explanation:

Step1: Isolate y

Solve the equation $x^{2}+y = 1$ for y. Subtract $x^{2}$ from both sides of the equation. $y=1 - x^{2}$

Step2: Check the function - definition

For every real - valued input x, there is exactly one output y. According to the definition of a function, if for each value of the independent variable x in the domain, there is exactly one value of the dependent variable y, then y is a function of x. Since for any real number x, substituting it into $y = 1 - x^{2}$ gives a single value of y, y is a function of x.

Answer:

A. Yes