Polynomial functions

Question

Describe the left and right behaviors of the following polynomial functions.

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.x^3 + 6x^3 - x^2

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

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

Answer 1

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

Leading exponent is even and leading coefficient is positive. Both ends will go to ∞

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

Leading exponent is odd and leading coefficient is positive.

As x->∞, y->∞ and As x->-∞, y->-∞

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

Leading exponent is odd and leading coefficient is positive.

As x->∞, y->∞ and As x->-∞, y->-∞

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

Leading exponent is odd and leading coefficient is negative.

As x->∞, y->-∞ and As x->-∞, y->∞

f(x) = -0.x^3 + 6x^3 - x^2

Why are there 2 terms that have the same exponent? Typo?

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

Leading exponent is even and leading coefficient is positive. Both ends will go to ∞

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

Your are missing a + or minus between the terms, cannot yell the sign of the leading coefficient.