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

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) here, usually the base of the common - logarithm is (a = 10>1)) is an increasing function.

Step2: Analyze end - behavior as (x) increases

As (x\to+\infty), (u=x - 2\to+\infty). Since (y = \log(u)) is an increasing function, when (u\to+\infty), (y=\log(u)\to+\infty). That is, as (x) increases, (f(x)=\log(x - 2)) moves toward positive infinity.

Step3: Analyze end - behavior as (x) decreases

As (x) approaches (2) from the right ((x\to2^{+})), (u=x - 2\to0^{+}). And (\log(x - 2)\to-\infty). As (x) decreases further from values greater than (2), the function value goes to negative infinity, not positive infinity or a constant.

Answer:

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