Polynomial functions

Question

Describe the left and right behaviors of the following functions.

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

All polynomial functions with coefficient of the highest power term greater than 0 go to positive infinity as x gets large; negative leading coefficient means negative infinity as x gets large.

The situation as x gets large negatively depends not only on the sign of leading coefficient but also on whether the highest power is odd or even...and I will leave that to you to think about.