Are odd functions symmetric about the origin?
Understand the Problem
The question is asking whether odd functions exhibit symmetry about the origin. This refers to the property of odd functions where for every point (x, f(x)), the point (-x, -f(x)) also exists, indicating that the graph of the function is symmetric in relation to the origin.
Answer
Yes, odd functions are symmetric about the origin.
The graph of an odd function is symmetric about the origin because the function satisfies the property -f(x) = f(-x). This means the graph of the function remains unchanged after a rotation of 180 degrees about the origin.
Answer for screen readers
The graph of an odd function is symmetric about the origin because the function satisfies the property -f(x) = f(-x). This means the graph of the function remains unchanged after a rotation of 180 degrees about the origin.
More Information
Odd functions exhibit rotational symmetry about the origin, which can be visualized by rotating their graph 180 degrees around the origin.
Tips
A common mistake is confusing symmetry about the origin with symmetry about the y-axis (which characterizes even functions). Make sure to verify the function satisfies -f(x) = f(-x).
Sources
- Odd Functions - Core Mathematics - ncl.ac.uk
- Even and odd functions - Wikipedia - en.wikipedia.org
- Odd Function - Definition, Properties, Graph, Examples - Cuemath - cuemath.com
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