Consider the polynomial function $h(x)=-2 x^{5}+8 x^{4}-2 x^{2}+15$. What is the end behavior of the graph of $h$ ?

Step 1 ：Consider the polynomial function \(h(x)=-2 x^{5}+8 x^{4}-2 x^{2}+15\).

Step 2 ：The end behavior of a polynomial function is determined by the degree and the leading coefficient of the polynomial. The degree of the polynomial is the highest power of x, and the leading coefficient is the coefficient of the term with the highest power.

Step 3 ：In this case, the degree is 5 (from the term -2x^5) and the leading coefficient is -2.

Step 4 ：Since the degree is odd and the leading coefficient is negative, the end behavior of the graph is: as x approaches positive infinity, h(x) approaches negative infinity and as x approaches negative infinity, h(x) approaches positive infinity.

Step 5 ：Final Answer: \(\boxed{\text{As } x \to \infty, h(x) \to -\infty \text{ and as } x \to -\infty, h(x) \to \infty}\)