select the correct answer. which function has an asymptote at x = 5 and an x - intercept of (6,0)? a…

Explanation:

Step1: Recall logarithm - asymptote property

The vertical asymptote of the function (y = \log(u)) occurs when (u = 0).

Step2: Check the asymptote for each option

For option A, if (y=\log(x - 5)), setting (x-5=0), we get (x = 5), so it has a vertical - asymptote at (x = 5). For option B, if (y=\log(x + 5)), setting (x + 5=0), we get (x=-5), so it has a vertical - asymptote at (x=-5). For option C, if (y=\log x-5), the vertical asymptote is at (x = 0) (since for (y=\log x), the asymptote is (x = 0)). For option D, if (y=\log x + 5), the vertical asymptote is at (x = 0) (since for (y=\log x), the asymptote is (x = 0)).

Step3: Check the x - intercept for option A

To find the x - intercept, set (y = 0). For (y=\log(x - 5)), when (y = 0), we have (\log(x - 5)=0). Since (\log1=0), then (x-5 = 1), which gives (x=6). So the x - intercept is ((6,0)).

Answer:

A. (f(x)=\log(x - 5))