Answer:
option B : [tex]f(x)= log_7(x-39)[/tex]
Step-by-step explanation:
(a) [tex]f(x) = 7^{x-39}[/tex]
For exponential function , there is no vertical asymptotes
General form of exponential function is
[tex]f(x) = n^{ax-b}+k[/tex]
[tex]f(x) = 7^{x-39}[/tex]
In the given f(x) the value of k =0
So horizontal asymptote is y=0
(b) lets check with option
[tex]f(x)= log_7(x-39)[/tex]
To find vertical asymptote we set the argument of log =0 and solve for x
Argument of log is x-39
x-39=0 so x=39
Hence vertical asymptote at x=39
