Final answer:
The end behavior of the function f(x)=7x⁵-4x³-9x+1 is that as x approaches positive infinity, the function increases without bound. As x approaches negative infinity, the function decreases without bound.
Step-by-step explanation:
The end behavior of a function describes what happens to the function as x approaches positive infinity and negative infinity.
To determine the end behavior of the function f(x)=7x⁵-4x³-9x+1, we can look at the highest degree term, which is 7x⁵.
Since the exponent is odd and the coefficient is positive, the end behavior of the function is:
As x approaches positive infinity, f(x) increases without bound.
As x approaches negative infinity, f(x) decreases without bound.