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.

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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:

  1. 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.
  2. 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).
  3. 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.

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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