How do you find the end behavior of #F(x) = 2x^(3) + 3x^(2) - 8x -12#?

Question

Lily Anderson · Accepted Answer

The end behaviour would be x#->oo, y->oo# and x#-> -oo, y->-oo# It is a cubic polynomial function with positive leading coefficient. Its graph would rise to the right and fall to the left. The end behaviour would thus be x#->oo, y->oo# and x#-> -oo, y->-oo#

Greyson Brown · Answer

undefined To find the end behavior of the function F(x) = 2x^3 + 3x^2 - 8x - 12:

1. Look at the leading term, which is 2x^3. 
2. Determine the degree of the polynomial, which is 3.
3. For odd-degree polynomials:
   - As x approaches positive infinity, F(x) approaches positive infinity.
   - As x approaches negative infinity, F(x) approaches negative infinity.

So, as x approaches positive infinity, F(x) increases without bound, and as x approaches negative infinity, F(x) decreases without bound.

Ariana Alvarez · Answer

undefined To find the end behavior of $ F(x) = 2x^3 + 3x^2 - 8x - 12 $, you examine the leading term, which is $ 2x^3 $. Since the degree of the polynomial is odd and the coefficient of the leading term is positive, the end behavior of the function is as follows:

As $ x $ approaches negative infinity, $ F(x) $ approaches negative infinity.
As $ x $ approaches positive infinity, $ F(x) $ approaches positive infinity.