Graph log of x+2

$\log (x + 2)$

Step 1

Find the asymptotes.

Set the argument of the logarithm equal to zero.

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

The vertical asymptote occurs at $x = - 2$ .

Vertical Asymptote: $x = - 2$

Step 2

Find the point at $x = - 1$ .

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

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

Simplify the result.

Add $- 1$ and $2$ .

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

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

$f (- 1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 8$ .

Replace the variable $x$ with $8$ in the expression.

$f (8) = \log ((8) + 2)$

Simplify the result.

Add $8$ and $2$ .

$f (8) = \log (10)$

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

$f (8) = 1$

The final answer is $1$ .

$1$

Convert $1$ to decimal.

$y = 1$

Step 4

Find the point at $x = 0$ .

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

$f (0) = \log ((0) + 2)$

Simplify the result.

Add $0$ and $2$ .

$f (0) = \log (2)$

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 $x = - 2$ and the points $(- 1, 0), (8, 1), (0, 0.30102999)$ .

Vertical Asymptote: $x = - 2$

$\begin{array}{c} x & y \\ - 1 & 0 \\ 0 & 0.301 \\ 8 & 1 \end{array}$

Step 6

Graph log of x+2

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