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

For the function $y = \log(u)$, the vertical - asymptote occurs when $u = 0$.

Step2: Check the asymptote for each option

For option A: $f(x)=\log(x - 5)$, setting $x-5=0$, we get $x = 5$ as the vertical asymptote. For option B: $f(x)=\log(x + 5)$, setting $x + 5=0$, we get $x=-5$ as the vertical asymptote. For option C: $f(x)=\log x-5$, the vertical asymptote is $x = 0$ (since for $y=\log x$, the asymptote is $x = 0$). For option D: $f(x)=\log x + 5$, the vertical asymptote is $x = 0$.

Step3: Check the x - intercept for option A

To find the x - intercept, set $y = 0$. For $f(x)=\log(x - 5)=0$, we know that if $\log a=0$, then $a = 1$ (since $\log_{10}1=0$). So, $x-5=1$, which gives $x=6$. The x - intercept is $(6,0)$.

Answer:

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