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

Solve the equation to find the coordinate for the absolute value vertex.

Subtract from both sides of the equation.

Multiply each term in by

Multiply each term in by .

Multiply .

Multiply by .

Multiply by .

Multiply by .

Replace the variable with in the expression.

Simplify .

Multiply by .

Subtract from .

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

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.

Multiply by .

Add and .

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

The final answer is .

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

Replace the variable with in the expression.

Simplify the result.

Subtract from .

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

The final answer is .

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

Replace the variable with in the expression.

Simplify the result.

Multiply by .

Subtract from .

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

The final answer is .

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

Graph y=|1-x|