Final answer:
The end behavior of the graph of the given function is as x approaches negative infinity, h(x) approaches positive infinity, and as x approaches positive infinity, h(x) approaches negative infinity.
Step-by-step explanation:
The end behavior of a polynomial function is determined by the highest degree term. In the given function, h(x)=-5x⁴+7x³-6x²+9x+2, the term with the highest degree is -5x⁴. Since the degree of the term is even and the coefficient is negative, the end behavior of the graph of h(x) is as follows:
As x approaches negative infinity, h(x) approaches positive infinity.
As x approaches positive infinity, h(x) approaches negative infinity.