# Graph y=x|x|+|x|-5x

Graph y=x|x|+|x|-5x
Simplify .
Move .
Reorder and .
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, .
Replace the variable with in the expression.
Simplify .
Simplify each term.
Multiply by .
The absolute value is the distance between a number and zero. The distance between and is .
Multiply by .
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:
For each value, there is one value. Select a 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.
Multiply by .
The absolute value is the distance between a number and zero. The distance between and is .
Multiply by .
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.
Multiply by .
The absolute value is the distance between a number and zero. The distance between and is .
Multiply by .
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.
Multiply by .
Multiply by .
The absolute value is the distance between a number and zero. The distance between and is .
The absolute value is the distance between a number and zero. The distance between and is .
Substitute the value into . In this case, the point is .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Multiply by .
The absolute value is the distance between a number and zero. The distance between and is .
Multiply by .
The absolute value is the distance between a number and zero. The distance between and is .