Question

Algebra 2 question, please help!

The degree of the polynomial function represented by the graph is (odd or even) , and its leading coefficient is (positive or negative) .

Answer 1

Even, then Negative due to limit

Explanation:

Answer 2

Let the leading term of the polynomial, f(x), be axⁿ.

Examine the possibilities.
n a x -> - ∞ x -> +∞
------- ---- ----------- ------------
even a>0 f -> +∞ f -> +∞ Not true
even a<0 f-> - ∞ f-> -∞ True
odd a>0 f-> -∞ f-> +∞ Not true
odd a<0 f-> +∞ f-> -∞ Not true

Answer:
(a) the degree of the polynomial is even, and
(b) the coefficient of the leading term is negative.