# The graph of a polynomial function has the following characteristics: a) Its domain and range are the set of all real numbers. b) There are turning po

The graph of a polynomial function has the following characteristics: a) Its domain and range are the set of all real numbers. b) There are turning points at $x=-2$, 0, and 3. a) Draw the graphs of two different polynomial functions that have these three characteristics. b) What additional characteristics would ensure that only one graph could be drawn?

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The other equation that works, is $f\left(x\right)=\frac{1}{4}{x}^{4}-\frac{1}{3}{x}^{3}-3{x}^{2}-1$.
a.) there are two polynomials that work for this situation.
The answer is a.) $f\left(x\right)=\frac{1}{4}{x}^{4}-\frac{1}{3}{x}^{3}-3{x}^{2}$