Question

determine whether the following equation defines y as a function of x.$x^{2}+y^{2}=121$does the equation $x^{2}+y^{2}=121$ define y as a function of x?yesno

Explanation:

Step1: Solve for y in terms of x

Start with the given equation:
$x^2 + y^2 = 121$
Rearrange to isolate $y^2$:
$y^2 = 121 - x^2$
Take square roots of both sides:
$y = \sqrt{121 - x^2} \text{ or } y = -\sqrt{121 - x^2}$

Step2: Apply function definition

A function requires that each input $x$ (in the domain) maps to exactly one output $y$. For any valid $x$ (e.g., $x=0$), we get two values: $y=11$ and $y=-11$.

Answer:

No