Sketch the graph of a 4th degree polynomial function f(x) such that f( 3) = 0, f( 1) = 0, f(1) = 0 , and f(3) = 0 and f(x) is increasing at extreme left.
Mathematics
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Question
Sketch the graph of a 4th degree polynomial function f(x) such that f( 3) = 0, f( 1) = 0, f(1) = 0 , and f(3) = 0 and f(x) is increasing at extreme left.
1 Answer

1. User Answers sqdancefan
Answer:
see attached
Stepbystep explanation:
For each listed root x=p as signified by f(p) = 0, the function has a factor (xp). The given roots and the given end behavior tell us the factored form is ...
f(x) = (x +3)(x +1)(x 1)(x 3)
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The graph is attached. It shows the function increasing at extreme left, crossing the xaxis at x=3, and again at x=1, x=1 and x=3. Since it crosses an even number of times, the rightside end behavior is "decreasing" toward negative infinity.