17.8k views
4 votes
What is the end behavior of the graph of the polynomial function y = 10x^9 - 4x

User Lutfi
by
8.5k points

1 Answer

0 votes

To describe the end behavior of a polynomial, we have to look at the leading term (term w/ the highest degree). The leading term in this polynomial is 10x^9.

If the power of the leading term is even, the function will approach infinity as x approaches both positive and negative infinity. (so both will point up)

If the power of the leading term is odd, the function will approach infinity as x approaches positive infinity and the function will approach negative infinity as x approaches negative infinity. (right side go up, left side go down)

We also need to consider the leading coefficient. If it is positive, the rules I stated above do not change. But if it is positive, it's basically the opposite. So for the first rule I stated both sides would point down. For the second rule, it would be right side go down and left side go up instead.

The power of the leading term is odd and the leading coefficient is positive, so the end behavior can be described as:

As x approaches infinity, the function will approach infinity. As x approaches negative infinity, the function will approach negative infinity. You can also say "y" instead of "the function".

User Gulam
by
7.5k points

No related questions found