Question

Which logarithmic function has x = 5 as its vertical asymptote and (6, 0) as the x-intercept? (x is the variable.)
The logarithmic function is f(x) = log ?

Answer 1

Well, a normal log(x) has a vertical asymptote at x=0, right?

Answer 2

To get the log function to have a vertical asymptote at x=5 all we have to do is shift it five units to the right.

Answer 3

so f(x)= log(x-5)

Answer 4

the reason it is minus five is because vertical and horizontal shifts the affect the x variable are always the opposite operation.

Answer 5

f(x) = log(x-5) automatically has 6 as its x-intercept as well, because log(6-5)=log(1)=0

Answer 6

not vertical

Answer 7

yes, since you are shifting the whole graph five units to the right , and the original log(x) had an x-int at (1,0), the x-int is also shifted five units to the right as well.