Determine the End Behavior

Question

Determine the end behavior of the following polynomial function:

f(x)=3(x−2)^13 (x−6)^9

1) The leading term of the polynomial is:

2) The degree of f(x) is:

3) The leading coefficient is:

Answer 1

f(x) = 3x²² + ...

1. Leading term is 3x²²
2. The degree of the polynomial is 22
3. Leading coefficient is 3
4. The end behavior (i.e.,the behavior of f(x) as x→±∞) is the same as the behavior of the leading term

As x→ ±∞, f(x) → ∞

Answer 2

3x²¹

21

3

As a function of odd degree x → -∞, y → -∞ and x → +∞, y → +∞