Pre-Algebra Examples

Graph y=(|x|)/x
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
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
The absolute value is the distance between a number and zero. The distance between and is .
Step 2.1.2.2
Divide by .
Step 2.1.2.3
The final answer is .
Step 2.2
Substitute the value into . In this case, the point is .
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Step 2.2.1
Replace the variable with in the expression.
Step 2.2.2
Simplify the result.
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Step 2.2.2.1
Divide by .
Step 2.2.2.2
The absolute value is the distance between a number and zero. The distance between and is .
Step 2.2.2.3
The final answer is .
Step 2.3
The absolute value can be graphed using the points around the vertex
Step 3