# Graph y=|x-5|-4

Find the absolute value vertex. In this case, the vertex for is .
To find the coordinate of the vertex, set the inside of the absolute value equal to . In this case, .
Add to both sides of the equation.
Replace the variable with in the expression.
Simplify .
Simplify each term.
Subtract from .
The absolute value is the distance between a number and zero. The distance between and is .
Subtract from .
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:
For each value, there is one value. Select few values from the domain. It would be more useful to select the values so that they are around the value of the absolute value vertex.
Substitute the value into . In this case, the point is .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Subtract from .
The absolute value is the distance between a number and zero. The distance between and is .
Subtract from .
Substitute the value into . In this case, the point is .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Subtract from .
The absolute value is the distance between a number and zero. The distance between and is .
Subtract from .
Substitute the value into . In this case, the point is .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Subtract from .
The absolute value is the distance between a number and zero. The distance between and is .
Subtract from .