What is domain and graph for $\frac{xy}{k}$?

Question

I have this function

$$q = \frac{xy}{k}$$

Where $k$ is a constant.

I don't understand if the domain should be $\mathbb{R}^2$ and, if it is, I don't understand why is $\mathbb{R}^2$ and not $\mathbb{R}$.

Answer 1

Notice that $$q = q(x, y) = \frac{xy}{k}$$

And $k$ is a constant, so it's not part of the unknown.

Since thou have a function in two variables, $x$ and $y$, it's obviously a function in $\mathbb{R}^2$.

For what concerns the domain, you have to split into $x$ and $y$:

$$\mathcal{D}: x\in\mathbb{R} ~~~ \wedge ~~~ y\in\mathbb{R}$$

($\wedge$ means "and").