Graph f(x) = log of x+1

$f (x) = \log (x + 1)$

Step 1

Find the asymptotes.

Set the argument of the logarithm equal to zero.

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

The vertical asymptote occurs at $x = - 1$ .

Vertical Asymptote: $x = - 1$

Step 2

Find the point at $x = 0$ .

Replace the variable $x$ with $0$ in the expression.

$f (0) = \log ((0) + 1)$

Simplify the result.

Add $0$ and $1$ .

$f (0) = \log (1)$

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

$f (0) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 9$ .

Replace the variable $x$ with $9$ in the expression.

$f (9) = \log ((9) + 1)$

Simplify the result.

Add $9$ and $1$ .

$f (9) = \log (10)$

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

$f (9) = 1$

The final answer is $1$ .

$1$

Convert $1$ to decimal.

$y = 1$

Step 4

Find the point at $x = 1$ .

Replace the variable $x$ with $1$ in the expression.

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

Simplify the result.

Add $1$ and $1$ .

$f (1) = \log (2)$

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

$\log (2)$

Convert $\log (2)$ to decimal.

$y = 0.30102999$

Step 5

The log function can be graphed using the vertical asymptote at $x = - 1$ and the points $(0, 0), (9, 1), (1, 0.30102999)$ .

Vertical Asymptote: $x = - 1$

$\begin{array}{c} x & y \\ 0 & 0 \\ 1 & 0.301 \\ 9 & 1 \end{array}$

Step 6

Graph f(x) = log of x+1

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