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
1 answer:
Answer:
see attached
Step-by-step explanation:
For each listed root x=p as signified by f(p) = 0, the function has a factor (x-p). 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 x-axis at x=-3, and again at x=-1, x=1 and x=3. Since it crosses an even number of times, the right-side end behavior is "decreasing" toward negative infinity.
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