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:
f(x)=f(x)f(-x) = -f(x)
This implies that if you rotate the graph of the function 180° about the origin, the graph remains unchanged. This is called origin symmetry.

Let me know if you would like a deeper explanation or examples.


Here are 5 related questions for further learning:

  1. What is the difference between odd and even functions in terms of symmetry?
  2. Can a function be both even and odd? Why or why not?
  3. How does the symmetry of an even function differ from that of an odd function?
  4. What happens to the symmetry of a function when you add or subtract odd and even functions?
  5. How can you test if a function is odd or even using its algebraic expression?

Tip: To determine if a function is odd, substitute x-x for xx in the function. If the result is f(x)-f(x), 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