How do you find the end behavior of # f(x) = (x+1)^2(x-1) #?
1 Answer
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Explanation:
The degree of the polynomial is
Since the degree is odd, you know that
Look at the mother functions:
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graph{x [-10, 10, -5, 5]}
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graph{x^2 [-10, 10, -5, 5]}
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graph{x^3 [-10, 10, -5, 5]}
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graph{x^4 [-10, 10, -5, 5]}
Let's examine a cubic: if we change the sign of the first term, what happens?
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graph{-x^3 [-10, 10, -5, 5]}
However, in our case, we know that the leading term will be positive, so the graph will start "down" and then go "up".
Its end behavior:
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We can check on a graph:
graph{(x+1)^2(x-1) [-10, 10, -5, 5]}
