# Which statement about the end behavior of the logarithmic function f(x) = log(x + 3) - 2 is true?

As x decreases, y moves toward the vertical asymptote at x = -3.

As x decreases, y moves toward the vertical asymptote at x = -1.

As x increases, y moves toward negative infinity.

As x decreases, y moves toward positive infinity.

**Solution:**

We know that x = 0 and log (x) is undefined for a logarithmic function. So there is a vertical asymptote at x = 0. There won’t be any changes in the vertical asymptote when we do logarithmic transformations

Consider an example log (x + 3) - 2

Let us begin with log (x)

When the x-value decreases, the y-value can never pass through the vertical asymptote as it is undefined and less than the value at the vertical asymptote. So it would converge closer but never reach there.

Let us transform the insides

log (x + 3)

The properties of domain is changed here

x + 3 > 0 and x > -3

x = - 3 is our new asymptote.

Therefore, the statement as x decreases, y moves toward the vertical asymptote at x = -3 is true.

## Which statement about the end behavior of the logarithmic function f(x) = log(x + 3) - 2 is true?

As x decreases, y moves toward the vertical asymptote at x = -3.

As x decreases, y moves toward the vertical asymptote at x = -1.

As x increases, y moves toward negative infinity.

As x decreases, y moves toward positive infinity.

**Summary: **

The statement about the end behavior of the logarithmic function f(x) = log(x + 3) - 2, as x decreases, y moves toward the vertical asymptote at x = -3 is true.