Question

Which is the ending behavior of the graph of the polynomial function F(x)=3x^6+30x^5+75x^4

Answer 1

A good way to find the end behaviors is to look at the number of the longest exponent in the equation. If it's even, then both ends go the same direction. If it's odd, then the ends go in two different directions. The highest exponent is even, so both ends go the same direction. Since the base of that highest exponent is a positive number, the effects aren't reversed, so the answer to this would be:
As x=-∞, y=∞; As x=∞, y=∞

Answer 2

A polynomial function involves solely non-negative integer powers of x, such as a quadratic, cubic, or equation function. We can define a polynomial and give it a generic definition.

• Its use of the longest digit in the equation is an excellent approach to identify the end behaviors.
• If it's even, both ends will point in the same direction, it's unusual, the sides will point in different directions.
• The highest exponent is even, both endpoints in the very same manner since the highest exponent's basis is a prime value, the consequences are not reversed.

Therefore, the answer is

As $x \to \infty, y \to - \infty$

As $x \to - \infty, \ y \to +\infty$"

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