Answer parts (a)-(e) for the function shown below.

a. Use the leading coefficient test to determine the graph’s end behavior. Which statement describes the be
?
A. The graph rises to the left and to the right.
B. The graph falls to the left and rises to the right.
C. The graph rises to the left and falls to the right.
D. The graph falls to the left and to the right.

To determine the end behavior of the function , we focus on the leading term, which is . The leading coefficient is positive (1), indicating that as approaches negative infinity ( ), will approach negative infinity. Conversely, as approaches positive infinity ( ), will also approach positive infinity. This leads to the conclusion that the graph falls to the left and rises to the right, making the correct answer:

B. The graph falls to the left and rises to the right.

Now let’s take a moment to appreciate how cubic functions, like our friend , can have such fascinating behaviors! They are often the rock stars of polynomial functions, showcasing a variety of twists and turns as they navigate through the coordinate plane. It’s almost like they have their own personality! You’ll often find that their end behavior, determined by the leading term, gives you the first clue about what to expect from their overall shape.