How do you find the end behavior of the following equation: g(x)-3x^3-2x

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Do you mean g(x) = -3x^3 - 2x? Do you see that the biggest exponent is a positive odd number 3? See it? This function is an odd-degree polynomial. However, since the leading coefficient of this odd-degree polynomial is negative (the leading coefficient is -3), then its end-behavior represents BOTH ENDS of the graph going in a downward direction. Think of a giant letter M to get an idea.