Extension: The highest-degree term of a function determines the end behavior of its graph. The lower-degree terms affect the behavior of the graph in other ways.

A. Click the button to reset the graph. Graph y = 0.5x^4. Note the shape of the graph. Next, set b to 2.0 to graph y = 0.5x^4+ 2x^3. What do you notice about the shape of the graph near the origin? (Hint: For comparison, look at the graph of y = 2x^3.)

B. Set b back to 0.0 and set c to -4.0 to graph y = 0.5x^4- 4x^2. What do you notice about the shape of this graph near the origin?

C. In general, why do you think the lower-degree terms have more influence near the origin, while the highest-degree term dominates farther away from the origin?