Answer
Vertical asymptotes: $\quad x = -\frac{2}{3}$ and $x = -1$
No removable discontinuities or holes.
Work Step by Step
To find the vertical asymptote, find the zeros of the denominator by setting each factor equal to zero and solving:
$3x + 2 = 0$
Subtract $2$ from both sides of the equation:
$3x = -2$
Divide both sides of the equation by $3$:
$x = -\frac{2}{3}$
$x + 1 = 0$
Subtract $1$ from each side of the equation:
$x = -1$
We have vertical asymptotes at $x = -\frac{2}{3}$ and $x = -1$ only if they are not zeros of the numerator. In this exercise, $x = -\frac{2}{3}$ and $x = -1$ are not zeros of the numerator; therefore, they are vertical asymptotes of this function. This also means that this function has no removable discontinuities or holes because there are no common zeros in the numerator and denominator.
