# Graph y=|2x+1|-3

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, .
Solve the equation to find the coordinate for the absolute value vertex.
Subtract from both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Move the negative in front of the fraction.
Replace the variable with in the expression.
Simplify .
Simplify each term.
Cancel the common factor of .
Move the leading negative in into the numerator.
Cancel the common factor.
Rewrite the expression.
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.
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 .
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 .