How do you describe the end behavior of y=8-x^3-2x^4?

2 Answers
May 28, 2018

See explanation.

Explanation:

To describe end behavior of a function you need to calculate the limits:

lim_{x->-oo}f(x)

and

lim_{x->+oo}f(x)

Here you get:

lim_{x->+-oo}(8-x^3-2x^4)=lim_{x->+-oo}(x^4*(-2-1/x+8/x^3))

If x goes to +-oo the fractions in the brackets go to zero, and x^4 goes to +oo, so the whole expression goes to -oo. Therfore we can say that as x goes to -oo or +oo the function goes to -oo

May 28, 2018

as x->oo, f(x)->-oo
as x->-oo, f(x)->-oo

Explanation:

y=8-x^3-2x^4

To determine the "end behavior" we need only consider the highest degree term because as x->oo the highest degree term dominates the function's behavior:

-2x^4

x^4 has very similar behavior to x^2 just grows more rapidly.

since the coefficient is negative the function's end behavior is decreasing, so we have determined:

f(x) = -2x^4-x^3+8

as x->oo, f(x)->-oo
as x->-oo, f(x)->-oo

graph{-2x^4-x^3+8 [-10.545, 9.455, -1.4, 8.6]}