Polynomial functions

Question

Describe the left and right behaviors of the following polynomial functions. Can you also tell me if the left and right behaviors go up or down?

f(x) = x^6 + 5x^3 + 7x^2 - x-2

f(x) = 2x^5 + 3x^2 - x+5

f(x) = 14x^2 + 7x^3

f(x) = -(x + 3)^3 (x-4)

f(x) = -0.2x^5 + 6x^3 - x^2

f(x) = -x^3 + 3x^2 + 12x^6 -8

f(x)=(x+2)^2 (x-5)^5

Answer 1

If the Leading Coefficient is EVEN and +, up↑left up↑right, is ODD + down↓left up↑right

If the Leading Coefficient is EVEN and -, down↓left down↓right, is ODD - up↑left down ↓right

For f(x) = x^6 + 5x^3 + 7x^2 - x-2, the Leading Coefficient is EVEN +, so it is up↑left up↑right

you do the rest.....

Answer 2

The basic shapes of polynomials follow a pattern. If you can identify the degree of the polynomial, then you can identify the end behavior without graphing.