What is the end behavior of the graph of the polynomial function f(x) = 2x^3 – 26x – 24?

Accepted Solution

Answer: Choice B


The graph of f(x) is shown in the attached image. Imagine we can plot a point anywhere on this curve. Also imagine that this point can slide around as if it is a car on a roller coaster track. If the car moves to the left, then it will go downward ultimately. This indicates that 
as x approaches -infinity, then y also approaches negative infinity
as [tex]x \to -\infty[/tex] then [tex]y \to -\infty[/tex]

If you move the car to the right then it will move upward. So,
as x approaches positive infinity, then y approaches positive infinity
as [tex]x \to \infty [/tex] then [tex]y \to \infty [/tex]

Combine all of this and that leads to choice B as the final answer

One way to describe this end behavior is:
"Falls to the left and rises to the right"