Question

Determine whether the equation$2\left|x\right|+y=0$ defines$\left(y\right)$ as a function of$\left(x\right)$.

Short answer

The given equation $2\left|x\right|+y=0$defines $\left(y\right)$as a function of $\left(x\right)$.

Step-by-step solution

Step 1. Write down the given equation.

The given equation is $2\left|x\right|+y=0$.

Step 2.Solve the given equation for (y) in terms of (x).

Solving the given equation,

$$\begin{gathered} 2\left|x\right|+y=0....\left(\text{Given}\right) \\ \text{or,}2\left|x\right|=-y \\ -2\left|x\right|=y\mathrm{....}\left(\text{Multiplyby}\left(-1\right)\right) \\ y=-2\left|x\right| \end{gathered}$$

Step 3. Description of steps.

By simplifying the given equation, we obtain$y=-2\left|x\right|$ from which it can be interpreted that for unique value of$\left(x\right)$ there exists a unique $\left(y\right)$. There for the given equation represents$\left(y\right)$ as a function of $\left(x\right)$, which can also be written in function form as $f\left(x\right)=-2\left|x\right|$.