Question

Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. -3x5 + 9x4 + 5x3 + 3https://www.desmos.com/calculator/rsotev49ri

Answer 1

@Directrix

Answer 2

The end behavior of -3x5 + 9x4 + 5x3 + 3 is determined by the term with the highest power of x. That term is called the dominant term because it is the boss and over the long haul determines what the function will do.

The other terms + 9x4 + 5x3 + 3 are along for the ride and do some interesting things but in the end as x increases without bound, the dominant term determines whether the graph will exit the first or fourth quadrant.

The dominant term also determines into which quadrant the function will make its entrance, Quad 2 or Quad 3.

Answer 3

Question:

In quadrants 2 and 3, x is negative.

So, for small values of x such as -10,000, will be value of -3x5 be positive or negative?

@Tazmaniadevil