8. describe the end behavior of ( f(x) = 0.25x^3 - x^2 - 1 ).
8. describe the end behavior of ( f(x) = 0.25x^3 - x^2 - 1 ).
Answer
Explanation:
Step1: Determine the leading term
The leading term of the polynomial (f(x)=0.25x^{3}-x^{2}-1) is (0.25x^{3}).
Step2: Analyze the degree and leading coefficient
The degree (n = 3) (odd) and the leading coefficient (a=0.25>0). When (x\to+\infty), for the term (y = ax^{n}) with (n) odd and (a>0), (y = 0.25x^{3}\to+\infty). When (x\to-\infty), for the term (y=ax^{n}) with (n) odd and (a > 0), (y=0.25x^{3}\to-\infty).
Answer:
As (x\to+\infty), (f(x)\to+\infty); as (x\to-\infty), (f(x)\to-\infty)