Graph y = log base 3 of 1-x

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

Step 1

Find the asymptotes.

Set the argument of the logarithm equal to zero.

$1 - x = 0$

Solve for $x$ .

Subtract $1$ from both sides of the equation.

$- x = - 1$

Divide each term in $- x = - 1$ by $- 1$ and simplify.

Divide each term in $- x = - 1$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 1}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 1}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 1}{- 1}$

Simplify the right side.

Divide $- 1$ by $- 1$ .

$x = 1$

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.

$f (0) = \log_{3} (1 - (0))$

Simplify the result.

Subtract $0$ from $1$ .

$f (0) = \log_{3} (1)$

Logarithm base $3$ of $1$ is $0$ .

$f (0) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$= 0$

Step 3

Find the point at $x = - 1$ .

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

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

Simplify the result.

Multiply $- 1$ by $- 1$ .

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

Add $1$ and $1$ .

$f (- 1) = \log_{3} (2)$

The final answer is $\log_{3} (2)$ .

$\log_{3} (2)$

Convert $\log_{3} (2)$ to decimal.

$= 0.63092975$

Step 4

Find the point at $x = - 2$ .

Replace the variable $x$ with $- 2$ in the expression.

$f (- 2) = \log_{3} (1 - (- 2))$

Simplify the result.

Multiply $- 1$ by $- 2$ .

$f (- 2) = \log_{3} (1 + 2)$

Add $1$ and $2$ .

$f (- 2) = \log_{3} (3)$

Logarithm base $3$ of $3$ is $1$ .

$f (- 2) = 1$

The final answer is $1$ .

$1$

Convert $1$ to decimal.

$= 1$

Step 5

The log function can be graphed using the vertical asymptote at $x = 1$ and the points $(0, 0), (- 1, 0.63092975), (- 2, 1)$ .

Vertical Asymptote: $x = 1$

$\begin{array}{c} x & y \\ - 2 & 1 \\ - 1 & 0.631 \\ 0 & 0 \end{array}$

Step 6

Graph y = log base 3 of 1-x

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