Answer
* Because the range is $(-\infty, \infty)$ this must be a polynomial of odd degree.
* Notice also that the polynomial becomes a large positive number as $x$ becomes a large positive number, so the leading coefficient must be positive .
* Finally, notice that it has four turning points and we know that a polynomial of degree $n$ has at most $n-1$ turning points. So the polynomial graphed in the Figure might be degree $5$, although it could also be of degree $7, 9,$ etc.
Work Step by Step
* Because the range is $(-\infty, \infty)$ this must be a polynomial of odd degree.
* Notice also that the polynomial becomes a large positive number as $x$ becomes a large positive number, so the leading coefficient must be positive .
* Finally, notice that it has four turning points and we know that a polynomial of degree $n$ has at most $n-1$ turning points. So the polynomial graphed in the Figure might be degree $5$, although it could also be of degree $7, 9,$ etc.