# SOLUTION: use the leading coefficient test determine the end behavior of the polynomial fuction f(x)=-2x^3+4x^2+2X-3

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 Question 208456: use the leading coefficient test determine the end behavior of the polynomial fuction f(x)=-2x^3+4x^2+2X-3Answer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website!Use the leading coefficient test determine the end behavior of the polynomial function ``` Here are the rules for determining end behavior on all polynomial functions: Find the leading term, which is the term with the largest exponent. 1. Is the leading term's coefficient positive? Then it goes up one the right end. 2. Is the leading terms' coefficient negative? Then it goes down on the right end. 3. Is the leading terms' exponent even? Then it goes the same way on the left end as it does on the right end. 4. Is the leading terms' exponent odd? Then it goes the opposite way on the left end than it does on the right end. Let's go thru those rules with your polynomial Find the leading term, which is the term with the largest exponent. That's 1. Is the leading term's coefficient positive? No, it's -2 and that is negative. 2. Is the leading terms' coefficient negative? Yes, for -2 is negative. Then it goes down on the right end. 3. Is the leading terms' exponent even? No, it's 3 which is odd. 4. Is the leading terms' exponent odd? Yes, for 3 is odd. Then it goes the opposite way on the left end than it does on the right end. Since it goes down on the right, it goes up on the left end. In a nutshell, the rules are: 1. positive coefficient, up on right end. 2. negative coefficient, down on right end. 3. even power, left end same as right end. 4. odd power, left end opposite from right end. Edwin```