Question

determine whether the following equation defines y as a function of x.
$x^2 + y^2 = 7$
does the equation $x^2 + y^2 = 7$ define y as a function of x?
○ yes
○ no

Explanation:

Step1: Isolate $y^2$

$y^2 = 7 - x^2$

Step2: Solve for $y$

$y = \pm\sqrt{7 - x^2}$

Step3: Check function definition

For a single valid $x$ (e.g., $x=0$), $y=\sqrt{7}$ and $y=-\sqrt{7}$, meaning one $x$ maps to two $y$-values.

Answer:

No