Question

select the correct answer.

which graph is the graph of the function \\(f(x) = \frac{x^2 + 6x + 8}{2x + 8}\\)?

Explanation:

Simplify the rational function

$$ f(x) = \frac{x^2 + 6x + 8}{2x + 8} = \frac{(x + 4)(x + 2)}{2(x + 4)} $$

Identify holes and asymptotes

$$
LATEXBLOCK0
$$

Analyze the given graph

$$
LATEXBLOCK1
$$

Answer:

• (A) The shown graph (with vertical asymptote at \(x = -4\) and horizontal asymptote at \(y = 0\))
• (B) A straight line graph of \(y = \frac{1}{2}x + 1\) with a hole at \((-4, -1)\) (Correct answer)