select the correct answer. which statement describes the end - behavior of this function? (f(x)=log(x - 2))…

select the correct answer. which statement describes the end - behavior of this function? (f(x)=log(x - 2)) a. as the value of (x) decreases, the value of (f(x)) moves toward positive infinity. b. as the value of (x) increases, the value of (f(x)) moves toward positive infinity. c. as the value of (x) increases, the value of (f(x)) moves toward negative infinity. d. as the value of (x) decreases, the value of (f(x)) moves toward a constant.

select the correct answer. which statement describes the end - behavior of this function? (f(x)=log(x - 2)) a. as the value of (x) decreases, the value of (f(x)) moves toward positive infinity. b. as the value of (x) increases, the value of (f(x)) moves toward positive infinity. c. as the value of (x) increases, the value of (f(x)) moves toward negative infinity. d. as the value of (x) decreases, the value of (f(x)) moves toward a constant.

Answer

Explanation:

Step1: Recall log - function properties

The domain of (y = \log(x - 2)) is (x>2). The general form of a logarithmic function (y=\log_a u) ((a > 1)) has the following end - behavior.

Step2: Analyze as (x) increases

As (x\to+\infty), (u=x - 2\to+\infty). For the function (y = \log(x - 2)) (assuming base (a>1)), when (u=x - 2) gets larger and larger, (\log(x - 2)\to+\infty).

Step3: Analyze as (x) decreases

As (x) approaches 2 from the right ((x\to2^{+})), (u=x - 2\to0^{+}), and (\log(x - 2)\to-\infty).

Answer:

B. As the value of (x) increases, the value of (f(x)) moves toward positive infinity.