Math Problem Statement
What type of symmetry does an odd function have?
Solution
This question asks about the symmetry property of odd functions. The correct answer is:
Odd functions have symmetry with respect to the origin.
Explanation:
An odd function satisfies the property:
This implies that if you rotate the graph of the function 180° about the origin, the graph remains unchanged. This is called origin symmetry.
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Here are 5 related questions for further learning:
- What is the difference between odd and even functions in terms of symmetry?
- Can a function be both even and odd? Why or why not?
- How does the symmetry of an even function differ from that of an odd function?
- What happens to the symmetry of a function when you add or subtract odd and even functions?
- How can you test if a function is odd or even using its algebraic expression?
Tip: To determine if a function is odd, substitute for in the function. If the result is , the function is odd!
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Math Problem Analysis
Mathematical Concepts
Functions
Symmetry
Odd and Even Functions
Formulas
f(-x) = -f(x)
Theorems
Origin Symmetry of Odd Functions
Suitable Grade Level
Grades 10-12