Answer
See graph and explanations.
Work Step by Step
Step 1. The graph has 5 turning points, which means that the degree should be at least 6.
Step 2. The end behavior shows that the graph falls on both the left and right sides. Thus, the leading term should be negative and an even power.
Step 3. We can write a polynomial as $f(x)=-x^6+14x^4-49x^2+36$
Step 4. We can plot the function as shown in the figure and we can see that it imitates the end behavior shown in the graph of the exercise.
