Final answer:
The end behavior of the polynomial function f(x) = x^4 + 5x^2 - 5x - 5 is such that as x approaches either positive or negative infinity, the function approaches positive infinity. This can be represented as:
As x → -∞, f(x) → +∞ and As x → +∞, f(x) → +∞
Step-by-step explanation:
The question asks about the end behavior of the polynomial function f(x) = x^4 + 5x^2 - 5x - 5. To determine the end behavior, we need to look at the highest degree term in the polynomial, as this term will dominate as x becomes very large or very small (positively or negatively infinite). Since the leading term is x^4, which is a positive term with an even power, both ends of the graph will rise up towards positive infinity.
Therefore, as x approaches positive or negative infinity, the function f(x) will also approach positive infinity. This is commonly written as:
limx→±∞ f(x) = ±∞
In summary, the end behavior of f(x) can be described as:
- As x approaches positive infinity, f(x) approaches positive infinity.
- As x approaches negative infinity, f(x) approaches positive infinity as well.