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Determine the end behavior of the function as x → +∞ and as x → −∞.

f(x) = 1000 − 39x + 51x^2 − 10x^3
As x → +∞, f(x) → ????
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As x → −∞, f(x) → ???

I know that the end behavior of the function is determined by the leading coefficient which in this case would be 10x^3? I just don't know what values I should plug into the answer box. Will the end function approaching both negative infinity and positive infinity just be positive?

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2 answers

  1. the "dominating" term is -10x^3 , not 10x^3

    so as x → +∞ , -10x^3 → -∞ , and
    as x→ -∞ , -10x^3 → +∞

    general appearance ...

    http://www.wolframalpha.com/input/?i=f%28x%29+%3D+1000+%E2%88%92+39x+%2B+51x%5E2+%E2%88%92+10x%5E3+

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  2. Thank you so much! I missed the negative part about the term which definitely impacted the answer.

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