Precalculus Examples

$f (x) = \log (3 x - 6)$

Step 1

Set the argument of the logarithm equal to zero.

$3 x - 6 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $6$ to both sides of the equation.

$3 x = 6$

Step 2.2

Divide each term in $3 x = 6$ by $3$ and simplify.

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Step 2.2.1

Divide each term in $3 x = 6$ by $3$ .

$\frac{3 x}{3} = \frac{6}{3}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{6}{3}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{3}$

$x = \frac{6}{3}$

$x = \frac{6}{3}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $6$ by $3$ .

$x = 2$

$x = 2$

$x = 2$

$x = 2$

Step 3

The vertical asymptote occurs at $x = 2$ .

Vertical Asymptote: $x = 2$

Step 4

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$