Sketch a graph, $f(x)$, that has the number and types of roots described for each situation below.

1. $5$ real roots

   Hint (a):

   Since the degree is an odd number, it will start and end in different directions.
   A real root occurs when the polynomial intersects the $x$-axis, so this graph should intersect the $x$-axis $5$ times.

2. $3$ real and $2$ complex roots

   Hint (b):

   This polynomial has $5$ roots, but only $3$ $x$-intercepts.

   Answer (b):

   A possible graph would be a polynomial with $3$ $x$-intercepts plus another bend.

3. $4$ complex roots

   Hint (c):

   The degree of this polynomial is even, so it starts and ends in the same direction.

4. $4$ complex and $2$ real roots

   Hint (d):

   See part (a), (b), and (c).