Graph y = natural log of 3x+4+3

Find where the expression ${\displaystyle \ln (3x+4)+3}$ is undefined.

Since ${\displaystyle \ln (3x+4)+3}$${\displaystyle \to }$${\displaystyle \infty }$ as ${\displaystyle x}$${\displaystyle \to }$${\displaystyle -\frac{4}{3}}$ from the left and ${\displaystyle \ln (3x+4)+3}$${\displaystyle \to }$${\displaystyle -\infty }$ as ${\displaystyle x}$${\displaystyle \to }$${\displaystyle -\frac{4}{3}}$ from the right, then ${\displaystyle x=-\frac{4}{3}}$ is a vertical asymptote.

Ignoring the logarithm, consider the rational function ${\displaystyle R\left(x\right)=\frac{a{x}^n}{b{x}^m}}$ where ${\displaystyle n}$ is the degree of the numerator and ${\displaystyle m}$ is the degree of the denominator.

There are no horizontal asymptotes because ${\displaystyle Q\left(x\right)}$ is ${\displaystyle 1}$.

No oblique asymptotes are present for logarithmic and trigonometric functions.

This is the set of all asymptotes.

Replace the variable ${\displaystyle x}$ with ${\displaystyle 0}$ in the expression.

Simplify the result.

Convert ${\displaystyle \ln \left(4\right)+3}$ to decimal.

Replace the variable ${\displaystyle x}$ with ${\displaystyle 1}$ in the expression.

Simplify the result.

Convert ${\displaystyle \ln \left(7\right)+3}$ to decimal.

Replace the variable ${\displaystyle x}$ with ${\displaystyle 2}$ in the expression.

Simplify the result.

Convert ${\displaystyle \ln \left(10\right)+3}$ to decimal.