Solve x²-4/9: Finding Where Function Values Are Negative

Find the positive and negative domains of the function below:

$y=x^2-\frac{4}{9}$

Determine for which values of $x$ the following is true:

$f(x) < 0$

To find where the function $y = x^2 - \frac{4}{9}$ is negative, solve the inequality:

$x^2 - \frac{4}{9} < 0$

This inequality simplifies to:

$x^2 < \frac{4}{9}$

Next, take the square root of both sides. Note the square root applies to both positive and negative values:

$-\frac{2}{3} < x < \frac{2}{3}$

Therefore, the values of $x$ for which the function $y = x^2 - \frac{4}{9}$ is negative are within the interval:

$-\frac{2}{3} < x < \frac{2}{3}$

Thus, the solution is correctly given by choice 2, with the interval $x$ such that:

$-\frac{2}{3} < x < \frac{2}{3}$