Question

Examine the graph of the logarithmic function f(x).

The function f(x) has a vertical asymptote at x= Blank.

Answer 1

The function f(x) has a vertical asymptote at x = 3

Explanation:

We can define an asymptote as an infinite aproximation to given value, such that the value is never actually reached.

For example, in the case of the natural logarithm, it is not defined for x = 0.

Then Ln(x) has an asymptote at x = 0 that tends to negative infinity, (but never reaches it, as again, Ln(x) is not defined for x = 0)

So a vertical asymptote will be a vertical tendency at a given x-value.

In the graph is quite easy to see it, it occurs at x = 3 (the graph goes down infinitely, never actually reaching the value x = 3)

Then:

The function f(x) has a vertical asymptote at x = 3