Answer:
Option A is correct.
Step-by-step explanation:
Let us graph the function [tex]f(x) = log(x + 3)-2[/tex] and analyze it.
The graph has one asymptote: the vertical [tex]x=-3[/tex]. With this information, let us analyze each of the options one by one.
Option A: As x decreases, y moves toward the vertical asymptote at x = -3.
This is true because as we move down along the x-axis to the left we meet the vertical asymptote [tex]x=-3[/tex].
Option B: As x decreases, y moves toward the vertical asymptote at [tex]x=-1[/tex].
This is incorrect since the vertical asymptote is not located at [tex]x=-1[/tex]
Option C: As x increases, y moves toward negative infinity.
No this is incorrect. As x increases, y moves towards positive infinity.
Option D: As x decreases, y moves toward positive infinity.
No this is incorrect. As x decreases, y moves towards negative infinity.
Thus only option A is correct.
