Do anyone know what the domain and vertical asymptote is for:
f(x)=4 ln(x)
domain is 4
To find the domain and vertical asymptote of the function f(x) = 4 ln(x), we need to consider the properties of the natural logarithm function.
1. Domain:
The natural logarithm function, ln(x), is defined only for positive real numbers. Therefore, the domain of f(x) = 4 ln(x) will be all positive real numbers. In interval notation, the domain can be expressed as (0, ∞).
2. Vertical Asymptote:
A vertical asymptote occurs when the function approaches positive or negative infinity as x approaches a certain value. This happens when the function is undefined at that point.
In the case of f(x) = 4 ln(x), there is no vertical asymptote for x > 0 because the natural logarithm is well-defined for all positive x-values.
However, at x = 0, the function ln(x) is not defined, which means it has a vertical asymptote at x = 0. This vertical asymptote occurs because the function approaches negative infinity as x approaches 0 from the right side.
To summarize:
- Domain: (0, ∞) (all positive real numbers)
- Vertical Asymptote: x = 0