Question

select the correct answer. which function has an asymptote at x = 5 and an x-intercept of (6,0)? a. f(x) = log(x − 5) b. f(x) = log(x + 5) c. f(x) = log x − 5 d. f(x) = log x + 5

Explanation:

Step1: Find vertical asymptote rule

For $\log(x - h)$, asymptote at $x=h$.

Step2: Match asymptote $x=5$

We need $h=5$, so function form $\log(x-5)$.

Step3: Verify x-intercept $(6,0)$

Substitute $x=6$ into $f(x)=\log(x-5)$:
$\log(6-5)=\log(1)=0$, which matches $(6,0)$.

Step4: Eliminate other options

• B: Asymptote at $x=-5$, incorrect.
• C: Asymptote at $x=0$, x-intercept at $x=10^5$, incorrect.
• D: Asymptote at $x=0$, x-intercept at $x=10^{-5}$, incorrect.

Answer:

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