Graph y=- log of x-2+3

Find where the expression ${\displaystyle -\log (x-2)+3}$ is undefined.

Since ${\displaystyle -\log (x-2)+3}$${\displaystyle \to }$${\displaystyle \infty }$ as ${\displaystyle x}$${\displaystyle \to }$${\displaystyle 2}$ from the left and ${\displaystyle -\log (x-2)+3}$${\displaystyle \to }$${\displaystyle \infty }$ as ${\displaystyle x}$${\displaystyle \to }$${\displaystyle 2}$ from the right, then ${\displaystyle x=2}$ 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 ${\displaystyle 3}$ in the expression.

Simplify the result.

Convert ${\displaystyle 3}$ to decimal.

Replace the variable ${\displaystyle x}$ with ${\displaystyle 12}$ in the expression.

Simplify the result.

Convert ${\displaystyle 2}$ to decimal.

Replace the variable ${\displaystyle x}$ with ${\displaystyle 4}$ in the expression.

Simplify the result.

Convert ${\displaystyle -\log \left(2\right)+3}$ to decimal.