Graph f(x) = log of x-3

$f (x) = \log (x - 3)$

Find the asymptotes.

Set the argument of the logarithm equal to zero.

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

The vertical asymptote occurs at $x = 3$ .

Vertical Asymptote: $x = 3$

Find the point at $x = 4$ .

Replace the variable $x$ with $4$ in the expression.

$f (4) = \log ((4) - 3)$

Simplify the result.

Subtract $3$ from $4$ .

$f (4) = \log (1)$

Logarithm base $10$ of $1$ is $0$ .

$f (4) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 13$ .

Replace the variable $x$ with $13$ in the expression.

$f (13) = \log ((13) - 3)$

Simplify the result.

Subtract $3$ from $13$ .

$f (13) = \log (10)$

Logarithm base $10$ of $10$ is $1$ .

$f (13) = 1$

The final answer is $1$ .

$1$

Convert $1$ to decimal.

$y = 1$

Find the point at $x = 5$ .

Replace the variable $x$ with $5$ in the expression.

$f (5) = \log ((5) - 3)$

Simplify the result.

Subtract $3$ from $5$ .

$f (5) = \log (2)$

The final answer is $\log (2)$ .

$\log (2)$

Convert $\log (2)$ to decimal.

$y = 0.30102999$

The log function can be graphed using the vertical asymptote at $x = 3$ and the points $(4, 0), (13, 1), (5, 0.30102999)$ .

Vertical Asymptote: $x = 3$

$\begin{array}{c} x & y \\ 4 & 0 \\ 5 & 0.301 \\ 13 & 1 \end{array}$