Graph y=-2 log base 2 of 4-x

$y = - 2 \log_{2} (4 - x)$

Step 1

Find the asymptotes.

Set the argument of the logarithm equal to zero.

${(4 - x)}^{2} = 0$

Solve for $x$ .

Set the $4 - x$ equal to $0$ .

$4 - x = 0$

Solve for $x$ .

Subtract $4$ from both sides of the equation.

$- x = - 4$

Divide each term in $- x = - 4$ by $- 1$ and simplify.

Divide each term in $- x = - 4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 4}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 4}{- 1}$

Simplify the right side.

Divide $- 4$ by $- 1$ .

$x = 4$

The vertical asymptote occurs at $x = 4$ .

Vertical Asymptote: $x = 4$

Step 2

Find the point at $x = 2$ .

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

$f (2) = - 2 \log_{2} (4 - (2))$

Simplify the result.

Multiply $- 1$ by $2$ .

$f (2) = - 2 \log_{2} (4 - 2)$

Subtract $2$ from $4$ .

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

Logarithm base $2$ of $2$ is $1$ .

$f (2) = - 2 \cdot 1$

Multiply $- 2$ by $1$ .

$f (2) = - 2$

The final answer is $- 2$ .

$- 2$

Convert $- 2$ to decimal.

$y = - 2$

Step 3

Find the point at $x = 3$ .

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

$f (3) = - 2 \log_{2} (4 - (3))$

Simplify the result.

Multiply $- 1$ by $3$ .

$f (3) = - 2 \log_{2} (4 - 3)$

Subtract $3$ from $4$ .

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

Logarithm base $2$ of $1$ is $0$ .

$f (3) = - 2 \cdot 0$

Multiply $- 2$ by $0$ .

$f (3) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 4

The log function can be graphed using the vertical asymptote at $x = 4$ and the points $(2, - 2), (3, 0)$ .

Vertical Asymptote: $x = 4$

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

Step 5

Graph y=-2 log base 2 of 4-x

Related Questions

Support LCMGCF.com by disabling your adblocker.