Final answer:
The end behavior of the graph of the function g(x) = 7x⁷ + 12x⁵-6x³-2x-18 is as follows: as x approaches negative infinity, g(x) approaches negative infinity; as x approaches positive infinity, g(x) approaches positive infinity.
Step-by-step explanation:
The end behavior of a polynomial function is determined by the degree of the highest power term and the leading coefficient. In the function g(x) = 7x⁷ + 12x⁵-6x³-2x-18, the highest power term is 7x⁷ and the leading coefficient is 7. Since the degree of the highest power term is odd and the leading coefficient is positive, the end behavior of the graph will be as follows:
As x approaches negative infinity, g(x) approaches negative infinity.
As x approaches positive infinity, g(x) approaches positive infinity.