Jacob F.

asked • 09/17/20

Describe the end behavior of the polynomial function using infinity notation.


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Alen M.

What is confusing to you about this question? I could answer it easily, but would rather attack the idea that you're struggling with, so you can solve it on your own.
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09/17/20

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Tracy D. answered • 09/17/20

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If you graph this equation, you will see a (hard to describe without a graph); but a long "S" on it's side (or rotated Counter Clock Wise 90 degrees), so it's pointing upward. I hope that helps with the visual.


For the end behavior, you will note this is an ODD function with a negative leading coefficient; so it will follow that as y (f(x)) increases, x will go toward negative infinity, and as y (f(x)) decreases, x will go toward positive infinity.

  1. f(x) → +∞, x → -∞
  2. f(x) → -∞, x → +∞


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Alen M.

You do not need a graph of this particular function to know end behavior, it suffices to know the elementary graphs of single term polynomials, ie x, x^2, x^3. Though the oddness of the function is a good point, I think it would be helpful to give the student insight about why the oddness of the function controls the end behavior. (Plug in some large numbers, notice how as the inputs increase, the smaller terms affect the overall value of the function less and less.) I'm new here, and I don't know what benefit you gain from answering questions, but if its only to help the student, I think a little more thought and care would go a long way.
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09/17/20

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