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Symmetry Calculator

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Example
Created on 2024-06-20Asked by Levi Moore (Solvelet student)
Determine if the function f(x)=x3−xf(x) = x^3 - x is symmetric about the origin.

Solution

To determine if the function f(x)=x3−xf(x) = x^3 - x is symmetric about the origin: 1. **Check for origin symmetry:** A function is symmetric about the origin if f(−x)=−f(x)f(-x) = -f(x). 2. **Compute f(−x)f(-x):** f(−x)=(−x)3−(−x)=−x3+x=−(x3−x)=−f(x). f(-x) = (-x)^3 - (-x) = -x^3 + x = -(x^3 - x) = -f(x). 3. **Result:** Since f(−x)=−f(x)f(-x) = -f(x), the function f(x)=x3−xf(x) = x^3 - x is symmetric about the origin. Solved on Solvelet with Basic AI Model
Some of the related questions asked by Elizabeth Roberts on Solvelet
1. Identify the type of symmetry (if any) possessed by the shape shown below. [Diagram: Symmetric figure]2. Determine if the function f(x)=x2+4x+4 f(x) = x^2 + 4x + 4 exhibits symmetry.,
DefinitionIn mathematics, symmetry is an invariance of a shape or operator under a set of transformations, such as reflection, rotation or translation. Example: A circle is symmetric with respect to its center; after any rotation with respect to the center, it will remain to the same shape.
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