Find the Asymptotes f(x) = natural log of x+3

Problem

ƒ(x)=ln(x+3)

Solution

1. Identify the type of function. The function ƒ(x)=ln(x+3) is a logarithmic function. Logarithmic functions of the form y=(log_b)(g(x)) do not have horizontal or oblique asymptotes.

2. Determine the domain. The argument of a natural logarithm must be strictly greater than zero.

x+3>0

x>−3

3. Find the vertical asymptote. A vertical asymptote occurs where the argument of the logarithm approaches zero from the right.

(lim_x→−3)(ln(x+3))=−∞

4. Conclude the location of the asymptote based on the limit. Since the function approaches negative infinity as x approaches −3 the line x=−3 is the vertical asymptote.

Final Answer

x=−3

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