Which statement about the end behavior of the logarithmic function f(x) = log(x + 3) – 2 is true?
a.
as x decreases, y moves toward the vertical asymptote at x = -3.
b.
as x decreases, y moves toward the vertical asymptote at x = -1.
c.
as x increases, y moves toward negative infinity.
d.
as x decreases, y moves toward positive infinity.

Option A is correct.

Step-by-step explanation:

Let us graph the function and analyze it.

The graph has one asymptote: the vertical . 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 .

Option B: As x decreases, y moves toward the vertical asymptote at .

This is incorrect since the vertical asymptote is not located at

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.

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