Odd or Even? Analyzing an Equation

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Homework Help Overview

The discussion revolves around identifying whether functions are odd or even, particularly focusing on polynomial expressions and their properties. Participants explore definitions and examples, questioning how to apply these concepts to various equations.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants attempt to clarify the definition of odd functions and question the implications of specific examples, such as x^3 and more complex expressions like (x^7)(x^6)/(x^4). There is also inquiry into how to determine the nature of functions defined piecewise.

Discussion Status

The discussion is active, with participants providing definitions and examples while seeking clarification on the application of these concepts. Some guidance has been offered regarding simplification and the nature of polynomial functions, but no consensus has been reached on all points raised.

Contextual Notes

Participants are navigating definitions and examples, with some confusion about the correct characterization of functions based on their algebraic forms. There is also mention of functions defined differently across intervals, adding complexity to the discussion.

UrbanXrisis
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the rule for an odd function is: -f(x)=f(x) correct?

however, x^3 is odd? Why is that? -(x^3) != (x^3)


Also, how would someone tell if a function is odd or even if it was an equation like: (x^7)(x^6)/(x^4) or something of that nature?
 
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UrbanXrisis said:
the rule for an odd function is: -f(x)=f(x) correct?

however, x^3 is odd? Why is that? -(x^3) != (x^3)


Also, how would someone tell if a function is odd or even if it was an equation like: (x^7)(x^6)/(x^4) or something of that nature?

You've got the definition wrong. You're essentially stating that -something = something. This is true only if something = 0.

Correct definition : If f(-x) = -f(x), then f is odd.
 
ahhh okay! That makes sense! What about telling if a function is odd or even if it was an equation like: (x^7)(x^6)/(x^4) or something similar to that?
 
UrbanXrisis said:
ahhh okay! That makes sense! What about telling if a function is odd or even if it was an equation like: (x^7)(x^6)/(x^4) or something similar to that?

What you've written can be simplified to x^9. (since [itex]x^ax^b = x^{a+b}[/itex])

Odd powers of a variable are odd functions. And even powers are even functions.
 
Plug in -x at the x place. If what comes out of f(-x) is EXACTLY -f(x), then your function is odd.
 
what if a function was...[(x^7)+(x^6)]/(x^4)
 
[itex]f(x) = x^3 + x^2[/itex] is neither odd nor even, (this is what your example simplifies to). See why this is true, by applying the definition.
 
Because the exponet is an odd and even number? So it's neither. Does the sign make any difference? Positive or negative? what if a function was...[(x^7)+(x^6)]/[(x^4)-(x^3)]
 
Read post #5.
 
  • #10
I get the point :smile: thanks
 
  • #11
What if the function is defined differently at different intervals? How would I then go about finding out whether it's odd or even?
 

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