Question

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

Answer 1

Answer: Choice B

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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 $x \to -\infty$ then $y \to -\infty$

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 $x \to \infty$ then $y \to \infty$

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"