Question

HELP PLEASE !!!!!!!!!!!

Answer 1

Answer:

option B

Step-by-step explanation:

$\lim_{x\to \infty} f(x) = \lim_{x \to \infty} (log(x+2)-3 )$

                    $= \lim_{x \to \infty} ( log(x+2)) - \lim_{x \to \infty} 3\\\\=\infty - 3\\\\= \infty$

$\lim_{x \to 2} f(x) = \lim_{x \to 2} ( log(x+2)) - \lim_{x \to2} 3$

                 $= log( 2 + 2 ) - 3\\\\= log 4 - 3\\\\=log(2^2) -3\\\\=2 log 2 -3$

$\lim_{x \to -2} f(x) = \lim_{x \to -2} ( log(x+2)) - \lim_{x \to -2} 3$  $\lim_{x \to -2}_+ f(x) = \lim_{x \to -2_+} ( log(x+2)) - \lim_{x \to -2_+} 3 = -\infty\\\\\lim_{x \to -2_-} f(x) = \lim_{x \to -2}_- ( log(x+2)) - \lim_{x \to -2}_- 3 = -\infty\\\\\\\lim_{x \to -2} f(x) = - \infty$