# Question #7b5bc

Jan 15, 2018

See explanation.

#### Explanation:

Given that $D \left(x\right) = 2 x$:

$D \left(x\right)$ is definitely a function since each input generates exactly one output. So that's true.

$x$ is the independent variable since you pick an $x$ and it determines $D \left(x\right)$.

$D \left(6\right) = 2 \cdot 6 = 12$ so $D \left(6\right) \ne 3$.

$D \left(x\right)$ is a direct variation since if we let $D \left(x\right) = y$ then $y = 2 x$ which is direct variation with constant $k = 2$

All of the points in the set $\left\{\begin{matrix}5 & 10 \\ 6 & 12 \\ - 2 & - 4\end{matrix}\right\}$ definitely fit the rule $y = 2 x$, so this one is true.