Question

determine whether the following equation defines y as a function of x.
$x^2 = 8y$
does the equation $x^2 = 8y$ define y as a function of x?
○ yes
○ no

Explanation:

Step1: Isolate $y$ in the equation

Rearrange $x^2 = 8y$ to solve for $y$:
$$y = \frac{x^2}{8}$$

Step2: Check function definition

For every input $x$, there is exactly one output $y$ calculated by squaring $x$ and dividing by 8. This satisfies the definition of a function (each $x$ maps to one unique $y$).

Answer:

Yes