To find the coordinate of the vertex, set the inside of the absolute value equal to . In this case, .

Replace the variable with in the expression.

Simplify .

Simplify each term.

The absolute value is the distance between a number and zero. The distance between and is .

Multiply by .

Add and .

The absolute value vertex is .

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

Set-Builder Notation:

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

The absolute value is the distance between a number and zero. The distance between and is .

Multiply by .

Add and .

The final answer is .

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

The absolute value is the distance between a number and zero. The distance between and is .

Multiply by .

Add and .

The final answer is .

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

The absolute value is the distance between a number and zero. The distance between and is .

Multiply by .

Add and .

The final answer is .

The absolute value can be graphed using the points around the vertex

Graph y=|3x|+1