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

The parent function:
f ( x ) = log x
Domain of a new function: x ∈ ( 5, +∞ )
Answer: f ( x ) = log ( x - 5 )

Answer 2

Answer: f ( x ) = log ( x - 5 )

Step-by-step explanation:

1) Take g(x) = log (x) as the parent function

2) The horizontal asymptote of g(x) is x = 0, and the y-intercept is (1,0).

3) Then, translating the asymptote to x = 5, and the y-intercept to (6,0), means that the graph of the parent function is being shifted 5 units to the right.

4) The rule is that the translation of the function g(x) a constant value to the right, say it is k, results in the function f(x) = g(x - k).

5) Therefore, the logarithmic function searched is f(x) = g(x - 5) = log (x - 5), and that is the answer.

6) You can prove that log (x - 5) meets the two conditions:

i)
`\lim_(x \to \\5+) log(x-5) = - \infty`, which means x = 5 is a vertical asymptote

ii) f(6) = log (6 - 5) = log (1) = 0 ⇒ point (6,0) is the x-intercept