Graph f(x) = log of 15-x

$f (x) = \log (15 - x)$

Step 1

Find the asymptotes.

Set the argument of the logarithm equal to zero.

$15 - x = 0$

Solve for $x$ .

Subtract $15$ from both sides of the equation.

$- x = - 15$

Divide each term in $- x = - 15$ by $- 1$ and simplify.

Divide each term in $- x = - 15$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 15}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 15}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 15}{- 1}$

Simplify the right side.

Divide $- 15$ by $- 1$ .

$x = 15$

The vertical asymptote occurs at $x = 15$ .

Vertical Asymptote: $x = 15$

Step 2

Find the point at $x = 14$ .

Replace the variable $x$ with $14$ in the expression.

$f (14) = \log (15 - (14))$

Simplify the result.

Multiply $- 1$ by $14$ .

$f (14) = \log (15 - 14)$

Subtract $14$ from $15$ .

$f (14) = \log (1)$

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

$f (14) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$= 0$

Step 3

Find the point at $x = 13$ .

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

$f (13) = \log (15 - (13))$

Simplify the result.

Multiply $- 1$ by $13$ .

$f (13) = \log (15 - 13)$

Subtract $13$ from $15$ .

$f (13) = \log (2)$

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

$\log (2)$

Convert $\log (2)$ to decimal.

$= 0.30102999$

Step 4

Find the point at $x = 12$ .

Replace the variable $x$ with $12$ in the expression.

$f (12) = \log (15 - (12))$

Simplify the result.

Multiply $- 1$ by $12$ .

$f (12) = \log (15 - 12)$

Subtract $12$ from $15$ .

$f (12) = \log (3)$

The final answer is $\log (3)$ .

$\log (3)$

Convert $\log (3)$ to decimal.

$= 0.47712125$

Step 5

The log function can be graphed using the vertical asymptote at $x = 15$ and the points $(14, 0), (13, 0.30102999), (12, 0.47712125)$ .

Vertical Asymptote: $x = 15$

$\begin{array}{c} x & y \\ 12 & 0.477 \\ 13 & 0.301 \\ 14 & 0 \end{array}$

Step 6

Graph f(x) = log of 15-x

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