Answer
Because the range is $(-\infty, \infty)$ this must be a polynomial of odd degree.
* Notice that it has six 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 $7$, although it could also be of degree $9, 11,$ etc.
* Finally, notice also that the polynomial becomes a large positive number as $x$ becomes a large positive number, so the leading coefficient must be positive .
Work Step by Step
Because the range is $(-\infty, \infty)$ this must be a polynomial of odd degree.
* Notice that it has six 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 $7$, although it could also be of degree $9, 11,$ etc.
* Finally, notice also that the polynomial becomes a large positive number as $x$ becomes a large positive number, so the leading coefficient must be positive .
