Question

use the leading coefficient test to determine whether y-->infinity) or y--> - infinity or x--->infinity

3.T

Answer 1

For a nth degree polynomial p(x):

i). When n is odd and the leading coefficient is positive, then p(x) → -∞ as x → -∞ and p(x) → ∞ as x → ∞.

ii). When n is odd and the leading coefficient is negative, then p(x) → ∞ as x → -∞ and p(x) → -∞ as x → ∞.

iii). When n is even and the leading coefficient is positive, then p(x) → ∞ as x → -∞ and p(x) → ∞ as x → ∞.

iv). When n is even and the leading coefficient is negative, then p(x) → -∞ as x → -∞ and p(x) → -∞ as x → ∞.

Here, p(x) = -3x⁴+5 is a polynomial of degree 4 (even) with a negative leading coefficient so that p(x) → -∞ as x → -∞ and p(x) → -∞ as x → ∞.

A graph of p(x) = -3x⁴+5 is attached for visual clarity.