Describe the end behavior of the polynomial function using lim f(x)and Iim f(x) x→∞ x→−∞ f(x)=5x2+x3+3x−2

Question

Describe the end behavior of the polynomial function using lim f(x)and Iim f(x)

x→∞ x→−∞

f(x)=5x2+x3+3x−2

Answer 1

Looking at the lead coefficient of the highest degree term, which is x³ we can see that it is positive. Since the highest degree term is a 3, this is a cubic function, and by definition cubic functions have opposite signs for end behavior.

If the leading coefficient is positive, as x approaches infinity, f(x) will approach positive infinity, and as x approaches negative infinity, f(x) will approach negative infinity.

Hope this helps.