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

$f (x) = - \log_{\frac{1}{3}} (x)$

Step 1

Find the asymptotes.

Set the argument of the logarithm equal to zero.

$x = 0$

The vertical asymptote occurs at $x = 0$ .

Vertical Asymptote: $x = 0$

Step 2

Find the point at $x = 1$ .

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

$f (1) = - \log_{\frac{1}{3}} (1)$

Simplify the result.

Logarithm base $\frac{1}{3}$ of $1$ is $0$ .

$f (1) = - 0$

Multiply $- 1$ by $0$ .

$f (1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 3$ .

Replace the variable $x$ with $3$ in the expression.

$f (3) = - \log_{\frac{1}{3}} (3)$

Simplify the result.

Logarithm base $\frac{1}{3}$ of $3$ is $- 1$ .

$f (3) = 1$

The final answer is $1$ .

$1$

Convert $1$ to decimal.

$y = 1$

Step 4

Find the point at $x = 9$ .

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

$f (9) = - \log_{\frac{1}{3}} (9)$

Simplify the result.

Logarithm base $\frac{1}{3}$ of $9$ is $- 2$ .

$f (9) = 2$

The final answer is $2$ .

$2$

Convert $2$ to decimal.

$y = 2$

Step 5

The log function can be graphed using the vertical asymptote at $x = 0$ and the points $(1, 0), (3, 1), (9, 2)$ .

Vertical Asymptote: $x = 0$

$\begin{array}{c} x & y \\ 1 & 0 \\ 3 & 1 \\ 9 & 2 \end{array}$

Step 6

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

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