select the correct answer.\nwhich statement describes the end - behavior of this function?\nf(x)=log(x…

select the correct answer.\nwhich statement describes the end - behavior of this function?\nf(x)=log(x - 2)\na. as the value of x decreases, the value of f(x) moves toward positive infinity.\nb. as the value of x increases, the value of f(x) moves toward positive infinity.\nc. as the value of x increases, the value of f(x) moves toward negative infinity.\nd. as the value of x decreases, the value of f(x) moves toward a constant.\nreset next

select the correct answer.\nwhich statement describes the end - behavior of this function?\nf(x)=log(x - 2)\na. as the value of x decreases, the value of f(x) moves toward positive infinity.\nb. as the value of x increases, the value of f(x) moves toward positive infinity.\nc. as the value of x increases, the value of f(x) moves toward negative infinity.\nd. as the value of x decreases, the value of f(x) moves toward a constant.\nreset next

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, assuming base - 10) is an increasing function.

Step2: Analyze end - behavior as (x) increases

As (x) increases without bound ((x\rightarrow+\infty)), (u=x - 2\rightarrow+\infty). Since (y = \log(u)) is an increasing function, as (u\rightarrow+\infty), (y=\log(u)\rightarrow+\infty).

Step3: Analyze end - behavior as (x) decreases

As (x) approaches 2 from the right ((x\rightarrow2^{+})), (u=x - 2\rightarrow0^{+}), and (\log(u)\rightarrow-\infty).

Answer:

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