# Graph y=1/2|x+2/3|+7 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, .
Since there is no variable to replace, the result 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 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 the numerator.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Move the negative in front of the fraction.
is approximately which is negative so negate and remove the absolute value
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Substitute the value into . In this case, the point is .
Replace the variable with in the expression.
Simplify the result.
Simplify the numerator.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Move the negative in front of the fraction.
is approximately which is negative so negate and remove the absolute value
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Multiply the numerator by the reciprocal of the denominator.
Multiply .
Multiply and .
Multiply by .
Substitute the value into . In this case, the point is .
Replace the variable with in the expression.
Simplify the result.
Simplify the numerator.
Write as a fraction with a common denominator.
Combine the numerators over the common denominator.
is approximately which is positive so remove the absolute value
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Multiply the numerator by the reciprocal of the denominator.
Multiply .
Multiply and .
Multiply by .
Substitute the value into . In this case, the point is .
Replace the variable with in the expression.
Simplify the result.
Simplify the numerator.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
is approximately which is positive so remove the absolute value
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.     