Math

Which describes the end behavior of the graph of the function f(x)=-2x^3-5x^2+x?

a. f(x) approaches infinity as x approaches negative infinity and f(x) approaches infinity as x approaches infinity
b. f(x) approaches negative infinity as x approaches negative infinity and f(x) approaches negative infinity as x approaches infinity
c. f(x) approaches infinity as x approaches negative infinity and f(x) approaches negative infinity as x approaches infinity
d. f(x) approaches negative infinity as x approaches negative infinity and f(x) approaches infinity as x approaches infinity

I do not understand end behavior and my lesson does not explain it very well. I also have no textbook for this class. Help is greatly appreciated. Thanks!

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  1. Pleaseee

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  2. end behavior is when x becomes very large (approaching infinity) in the positive and negative directions

    the behavior is driven by the term with the largest exponent ... in this case, the x cubed term

    the odd power means that x^3 has the same sign as x

    the negative coefficient (-2) changes the sign, so that at the ends, f(x) has the opposite sign of x

    read the answers carefully, and one will fit the bill

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  3. Is it d?

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  4. I am pretty sure it's right can you please check?

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  5. in d, are the signs for x and f(x) the same or different

    did you read my first response/explanation?

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