What is the end behavior of the polynomial function 2x^7 – 8x^6 + 3x^5 – 3?

The end behavior of a polynomial function is determined by its leading term, which is the term with the highest degree. For the polynomial given, 2x⁷ – 8x⁶ + 3x⁵ – 3, the leading term is 2x⁷.

Since the leading term 2x⁷ has a degree of 7 (which is odd) and a positive coefficient (2), we can deduce the end behavior of the graph:

• As x approaches positive infinity (x → ∞), the value of the polynomial will also approach positive infinity (f(x) → ∞).
• As x approaches negative infinity (x → -∞), the value of the polynomial will approach negative infinity (f(x) → -∞).

In summary, the end behavior of the graph of the polynomial function 2x⁷ – 8x⁶ + 3x⁵ – 3 is that it rises to the right and falls to the left.