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.

Add to 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 .

Replace the variable with in the expression.

Simplify .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Simplify by subtracting numbers.

Subtract from .

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:

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Multiply by .

Subtract from .

The absolute value is the distance between a number and zero. The distance between and is .

The final answer is .

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Multiply by .

Subtract from .

The absolute value is the distance between a number and zero. The distance between and is .

The final answer is .

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Multiply by .

Subtract from .

The absolute value is the distance between a number and zero. The distance between and is .

The final answer is .

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Multiply by .

Subtract from .

The absolute value is the distance between a number and zero. The distance between and is .

The final answer is .

The absolute value can be graphed using the points around the vertex

Graph f(x)=|3x-4|