Question

find the dicontinuities of the function.

\\(f(x) = \frac{x^2 + 12x + 27}{x^2 + 4x + 3}\\)

there is a removable discontinuity at
\\((-3, -3)\\).

where is the vertical asymptote(s)?

\\(\bigcirc\\) \\(x = -3, x = -1\\)
\\(\bigcirc\\) \\(x = -1\\)
\\(\bigcirc\\) \\(x = -9\\)
\\(\bigcirc\\) \\(x = -9, x = -3\\)

Explanation:

Factor the numerator and denominator

Using the Polynomial Factoring knowledge point

$$ f(x) = \frac{x^2 + 12x + 27}{x^2 + 4x + 3} = \frac{(x + 3)(x + 9)}{(x + 3)(x + 1)} $$

Identify the removable discontinuity

Using the Removable Discontinuities knowledge point

$$
LATEXBLOCK0
$$

Identify the vertical asymptote

Using the Vertical Asymptotes knowledge point

$$
LATEXBLOCK1
$$

Answer:

• \(x = -3, x = -1\)
• \(x = -1\) (Correct answer)
• \(x = -9\)
• \(x = -9, x = -3\)