Question

Describe the end behavior of f(x)=-x^5+4x^3-2x-2

Answer 1

Answer:

As x→∞, f(x)→∞

and as x→-∞, f(x)→-∞

Step-by-step explanation:

View Image.

Your first step is to look at the highest value exponent.

In this case it's x⁵.

If the highest exponent is an odd number, the graph will look like a sideway S as shown in the picture below. You can see as you move farther to the right, the y value approaches positive  infinity hence "As x→∞, f(x)→∞".

As you move farther left, the graph reaches negative infinity, hence "as x→-∞, f(x)→-∞".

Anyway, if your exponent were to be an even number then you're graph would look like a parabola (looks like a letter U) and f(x) would reach positive infinity when moving to the right side and left side.