Question

determine whether the following equation defines y as a function of x.
$x^{2}+y^{2}=4$
does the equation $x^{2}+y^{2}=4$ define y as a function of x?
\bigcirc yes
\bigcirc no

Explanation:

Step1: Rearrange for y

$y^2 = 4 - x^2$

Step2: Solve for y

$y = \pm\sqrt{4 - x^2}$

Step3: Check function definition

A function requires one y per x. Here, for $x$ values where $4-x^2>0$, there are two distinct y-values (positive and negative square roots).

Answer:

No