Calculus Examples

Find the Symmetry y=x^2
Step 1
There are three types of symmetry:
1. X-Axis Symmetry
2. Y-Axis Symmetry
3. Origin Symmetry
Step 2
If exists on the graph, then the graph is symmetric about the:
1. X-Axis if exists on the graph
2. Y-Axis if exists on the graph
3. Origin if exists on the graph
Step 3
Check if the graph is symmetric about the -axis by plugging in for .
Step 4
Since the equation is not identical to the original equation, it is not symmetric to the x-axis.
Not symmetric to the x-axis
Step 5
Check if the graph is symmetric about the -axis by plugging in for .
Step 6
Simplify.
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Step 6.1
Apply the product rule to .
Step 6.2
Raise to the power of .
Step 6.3
Multiply by .
Step 7
Since the equation is identical to the original equation, it is symmetric to the y-axis.
Symmetric with respect to the y-axis
Step 8
Check if the graph is symmetric about the origin by plugging in for and for .
Step 9
Simplify.
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Step 9.1
Apply the product rule to .
Step 9.2
Raise to the power of .
Step 9.3
Multiply by .
Step 10
Since the equation is not identical to the original equation, it is not symmetric to the origin.
Not symmetric to the origin
Step 11
Determine the symmetry.
Symmetric with respect to the y-axis
Step 12