State the degree number of terms and describe the long term

State the degree, number of terms, and describe the long term behavior of the function: y = 1 - 2x^4 + x^3

Solution

y=1-2x^4 +x^3

Here the highest exponent is 4. Therefore degree is 4

And number of terms =3

Here the degree is 4 which is even and leading coefficient is -2 which is negative .

Therefore

as x-> infinity, y->- infinity

as x->- infinity, y->- infinity