Answer:
The end behavior of the graph of p is:
f(x) → ∞ as x → -∞ and f(x) → -∞ as x → ∞
Step-by-step explanation:
Given the polynomial function
[tex]p\left(x\right)=\:-9x^9\:+6x^6\:-3x^3\:+1[/tex]
Since the leading term of the polynomial (the term in a polynomial that contains the highest power of the variable) is -9x⁹, then the degree is 9 i.e. odd, and the leading coefficient is -9, i.e. negative.
This means that f(x) → ∞ as x → -∞ and f(x) → -∞ as x → ∞
The graph is also attached below.
Thus, the end behavior of the graph of p is:
f(x) → ∞ as x → -∞ and f(x) → -∞ as x → ∞
