Pre-Algebra Examples

Graph (|x-2|)/(x-2)
Step 1
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.
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Step 1.1
Set the denominator in equal to to find where the expression is undefined.
Step 1.2
Add to both sides of the equation.
Step 1.3
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Interval Notation:
Set-Builder Notation:
Step 2
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.
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Step 2.1
Substitute the value into . In this case, the point is .
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Step 2.1.1
Replace the variable with in the expression.
Step 2.1.2
Simplify the result.
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Step 2.1.2.1
Simplify the numerator.
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Step 2.1.2.1.1
Subtract from .
Step 2.1.2.1.2
The absolute value is the distance between a number and zero. The distance between and is .
Step 2.1.2.2
Simplify the expression.
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Step 2.1.2.2.1
Subtract from .
Step 2.1.2.2.2
Divide by .
Step 2.1.2.3
The final answer is .
Step 2.2
The absolute value can be graphed using the points around the vertex
Step 3