# Graph f(x)=- log base 3 of x-1+3

Find where the expression is undefined.

The vertical asymptotes occur at areas of infinite discontinuity.

Ignoring the logarithm, consider the rational function where is the degree of the numerator and is the degree of the denominator.

1. If , then the x-axis, , is the horizontal asymptote.

2. If , then the horizontal asymptote is the line .

3. If , then there is no horizontal asymptote (there is an oblique asymptote).

There are no horizontal asymptotes because is .

No Horizontal Asymptotes

No oblique asymptotes are present for logarithmic and trigonometric functions.

No Oblique Asymptotes

This is the set of all asymptotes.

Vertical Asymptotes:

No Horizontal Asymptotes

Vertical Asymptotes:

No Horizontal Asymptotes

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Subtract from .

Logarithm base of is .

Multiply by .

Add and .

The final answer is .

Convert to decimal.

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Subtract from .

Logarithm base of is .

Multiply by .

Add and .

The final answer is .

Convert to decimal.

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Subtract from .

Logarithm base of is .

Multiply by .

Add and .

The final answer is .

Convert to decimal.

The log function can be graphed using the vertical asymptote at and the points .

Vertical Asymptote:

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