# Graph y=| natural log of x| 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.
To solve for , rewrite the equation using properties of logarithms.
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Solve for .
Rewrite the equation as .
Anything raised to is .
Replace the variable with in the expression.
Simplify .
The natural logarithm of is .
The absolute value is the distance between a number and zero. The distance between and is .
The absolute value vertex is .
Find the domain for so that a list of values can be picked to find a list of points, which will help graphing the absolute value function.
Set the argument in greater than to find where the expression is defined.
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
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.
is approximately which is positive so remove the absolute value
Substitute the value into . In this case, the point is .
Replace the variable with in the expression.
Simplify the result.
is approximately which is positive so remove the absolute value     