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Question

Use the Leading Coefficient Test to determine the right-hand and left-hand behavior of the graph of the polynomial function. $f(x)=2 x^{3}-3 x^{2}+x-1$

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To determine the end behavior of the graph of the polynomial function, we can apply the leading coefficient test. The end behavior of the functions can be determined in two ways. The first is to look for the leading coefficient of the function that contains the largest exponent; if the leading coefficient is "positive", the graph will rise to the right, and if the leading coefficient is "negative", the graph will fall to the right. Next, search for the degree of exponent of the leading coefficient to determine the function's left behavior. If the degree is "odd," the graph's end behavior will be the opposite of the right side, and if the degree is "even," the graph's end behavior will be the same as the right side.

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