Algebra Examples

$y = 3 \cot (π x)$

Step 1

Set the argument in $\cot (π x)$ equal to $π n$ to find where the expression is undefined.

$π x = π n$ , for any integer $n$

Step 2

Divide each term in $π x = π n$ by $π$ and simplify.

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Step 2.1

Divide each term in $π x = π n$ by $π$ .

$\frac{π x}{π} = \frac{π n}{π}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $π$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{π x}{π} = \frac{π n}{π}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{π n}{π}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $π$ .

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Step 2.3.1.1

Cancel the common factor.

$x = \frac{π n}{π}$

Step 2.3.1.2

Divide $n$ by $1$ .

$x = n$

Step 3

The domain is all values of $x$ that make the expression defined.

Set-Builder Notation:

${x | x \neq n}$ , for any integer $n$

Step 4

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${y | y \in ℝ}$

Step 5

Determine the domain and range.

Domain: ${x | x \neq n}$ , for any integer $n$

Range: $(- \infty, \infty), {y | y \in ℝ}$

Step 6