Question

consider the following relation.
3x² + 2x = -2x + 4y
step 3 of 3 : determine the implied domain of the function found in the first step. express your answer in interval notation.

Explanation:

Step1: Rewrite as function of $x$

Solve $3x^2 + 2x = -2x + 4y$ for $y$:

$$\begin{align*} 4y&=3x^2 + 2x + 2x\\ 4y&=3x^2 + 4x\\ y&=\frac{3x^2 + 4x}{4} \end{align*}$$

Step2: Identify domain restrictions

The function is a polynomial. Polynomials have no restrictions on $x$ (no division by zero, no square roots of negative numbers, etc.). All real numbers are allowed.

Step3: Write in interval notation

The set of all real numbers in interval notation is $(-\infty, \infty)$.

Answer:

$(-\infty, \infty)$