Graph y = log of 1/2x

$y = \log (\frac{1}{2} x)$

Step 1

Find the asymptotes.

Set the argument of the logarithm equal to zero.

$\frac{x}{2} = 0$

Set the numerator equal to zero.

$x = 0$

The vertical asymptote occurs at $x = 0$ .

Vertical Asymptote: $x = 0$

Step 2

Find the point at $x = 2$ .

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

$f (2) = \log (\frac{1}{2} \cdot (2))$

Simplify the result.

Cancel the common factor of $2$ .

Cancel the common factor.

$f (2) = \log (\frac{1}{2} \cdot 2)$

Rewrite the expression.

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

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

$f (2) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 1$ .

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

$f (1) = \log (\frac{1}{2} \cdot (1))$

Simplify the result.

Multiply $\frac{1}{2}$ by $1$ .

$f (1) = \log (\frac{1}{2})$

The final answer is $\log (\frac{1}{2})$ .

$\log (\frac{1}{2})$

Convert $\log (\frac{1}{2})$ to decimal.

$y = - 0.30102999$

Step 4

Find the point at $x = 3$ .

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

$f (3) = \log (\frac{1}{2} \cdot (3))$

Simplify the result.

Combine $\frac{1}{2}$ and $3$ .

$f (3) = \log (\frac{3}{2})$

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

$\log (\frac{3}{2})$

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

$y = 0.17609125$

Step 5

The log function can be graphed using the vertical asymptote at $x = 0$ and the points $(2, 0), (1, - 0.30102999), (3, 0.17609125)$ .

Vertical Asymptote: $x = 0$

$\begin{array}{c} x & y \\ 1 & - 0.301 \\ 2 & 0 \\ 3 & 0.176 \end{array}$

Step 6

Graph y = log of 1/2x

Related Questions

Support LCMGCF.com by disabling your adblocker.