Math Problem Statement
Which of the following functions exhibits odd symmetry?
Solution
To determine which function exhibits odd symmetry, we need to recall the condition for odd symmetry in a function . A function is considered odd if:
This means that for every term in the function, the powers of must be odd. Let's analyze each option:
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- Since , this is not odd.
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- , so this is also not odd.
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- Since , this function is odd.
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- , so it is not odd.
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- , so it is not odd.
Thus, the correct answer is:
, which exhibits odd symmetry.
Would you like further details or have any questions?
Here are some follow-up questions:
- What are the conditions for a function to be even?
- How can we verify symmetry in more complex functions?
- What is the difference between even and odd symmetry in practical applications?
- How do power functions relate to the symmetry of a function?
- Can a function exhibit both even and odd symmetry?
Tip: Functions with only odd-powered terms tend to exhibit odd symmetry.
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Math Problem Analysis
Mathematical Concepts
Function Symmetry
Odd Symmetry
Formulas
f(-x) = -f(x)
Theorems
Odd function property
Suitable Grade Level
High School