Graph f(x)=1/2 log of x

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

Find the asymptotes.

Set the argument of the logarithm equal to zero.

$x^{\frac{1}{2}} = 0$

Solve for $x$ .

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

${(x^{\frac{1}{2}})}^{2} = 0^{2}$

Simplify the exponent.

Simplify the left side.

Simplify ${(x^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{2} \cdot 2} = 0^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 0^{2}$

Rewrite the expression.

$x^{1} = 0^{2}$

Simplify.

$x = 0^{2}$

Simplify the right side.

Raising $0$ to any positive power yields $0$ .

$x = 0$

The vertical asymptote occurs at $x = 0$ .

Vertical Asymptote: $x = 0$

Find the point at $x = 1$ .

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

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

Simplify the result.

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

$f (1) = \frac{1}{2} \cdot 0$

Multiply $\frac{1}{2}$ by $0$ .

$f (1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify $\frac{1}{2} \log (2)$ by moving $\frac{1}{2}$ inside the logarithm.

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

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

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

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

$y = 0.15051499$

Find the point at $x = 3$ .

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

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

Simplify the result.

Simplify $\frac{1}{2} \log (3)$ by moving $\frac{1}{2}$ inside the logarithm.

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

The final answer is $\log (3^{\frac{1}{2}})$ .

$\log (3^{\frac{1}{2}})$

Convert $\log (3^{\frac{1}{2}})$ to decimal.

$y = 0.23856062$

The log function can be graphed using the vertical asymptote at $x = 0$ and the points $(1, 0), (2, 0.15051499), (3, 0.23856062)$ .

Vertical Asymptote: $x = 0$

$\begin{array}{c} x & y \\ 1 & 0 \\ 2 & 0.151 \\ 3 & 0.239 \end{array}$

Graph f(x)=1/2 log of x

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