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"