Even and Odd Functions Using Exponents
Description/Explanation/Highlights
Even and Odd Functions Using Exponents Video Description
This video explains how to determine if a function is even, odd, or neither as a result of looking at the exponents.
Steps and Key Points to Remember About Even and Odd Functions
To use exponents to determine if a function is even, odd, or neither, follow the steps shown below:
- First, look at all of the exponents of the function. If all of the exponents are odd, the function is likewise odd. \(f(x)=2x^5+3x^3+2x\) is odd since the exponents (5, 3, & 1) are alsonall odd.
- Moreover, if every exponent is even, the function is likewise even. \(f(x)=x^4+3x^2-4\) is even in the same way, since every exponent is also even (4, 2, & 0).
- Furthermore, if the exponents are mixed, the function is similarly, neither. Therefore, the function, \(f(x)=2x^3-x^2+x\) is also neither. The exponents 3 & 1 are odd but the exponent 2 is even.
Here are some key points to keep in mind:
- Exponents on variables are all even on even functions.
- Further, all exponents are odd on an odd function.
- Finally, functions are neither when there is a mix of even and odd exponents.
- A constant without a variable has a variable with an exponent of 0. It is therefore considered to be even when applying the rules.
- This can be shown Algebraically and that explanation is found in another video. Click here to watch the video on how to solve Algebraically.
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Video Highlights
- 00:00 Introduction
- 00:09 The process explained
- 00:30 Example of an odd function
- 00:56 Example of an even function
- 01:16 Example of a function that is neither
- 02:02 Conclusion
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