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

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

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

Answer

Explanation:

Step1: Analyze the vertical asymptote

For the function (y = \log(u)), the vertical asymptote is at (u = 0). For option A: (u=x - 5), the vertical asymptote is (x-5=0), so (x = 5). For option B: (u=x + 5), the vertical asymptote is (x+5=0), so (x=-5). For option C: (y=\log x-5), the vertical asymptote is (x = 0). For option D: (y=\log x + 5), the vertical asymptote is (x = 0).

Step2: Analyze the (x) - intercept

The (x) - intercept occurs when (y = 0). For option A: Set (y=\log(x - 5)=0). Since (\log a=0) implies (a = 1) (because (\log_{10}1=0)), then (x-5=1), so (x=6).

Answer:

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