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

Question

Nat2105 [25]

2 years ago

7

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

1 answer:

fenix001 [56] · Answer 1 · 2023-05-07T08:35:13+03:00

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.