What are the characteristics of the function $f(x)=2(x-4)^{5}$ ?
A. The left end of the graph of the function goes down, and the right end goes up.

B. It is a vertical stretch and a translation to the right of the parent function.
C. It is a reflection and a translation to the right of the parent function.
D. It has 5 zeros and at most 4 relative maximums or minimums.
E. Both ends of the graph of the function go up.
F. It has 4 zeros and at most 5 relative maximums or minimums.

Step 1 ：The function \(f(x)=2(x-4)^{5}\) is a polynomial function of degree 5. The characteristics of the function can be determined by analyzing the degree and the leading coefficient of the polynomial.

Step 2 ：The degree of the polynomial is 5, which is odd. Therefore, the ends of the graph of the function go in opposite directions. Since the leading coefficient is positive, the left end of the graph goes down, and the right end goes up.

Step 3 ：The function is a vertical stretch of the parent function \(f(x)=x^{5}\) by a factor of 2.

Step 4 ：The function is a translation of the parent function \(f(x)=x^{5}\) to the right by 4 units.

Step 5 ：The function has only one zero at x=4. This is because the factor \((x-4)\) is raised to the power of 5, which means it is repeated 5 times. Therefore, the function touches the x-axis at x=4 but does not cross it.

Step 6 ：The function has at most 4 relative maximums or minimums. This is because a polynomial function of degree n has at most n-1 relative maximums or minimums.

Step 7 ：\(\boxed{\text{Final Answer: The characteristics of the function } f(x)=2(x-4)^{5} \text{ are:}}\)

Step 8 ：A. The left end of the graph of the function goes down, and the right end goes up.

Step 9 ：B. It is a vertical stretch and a translation to the right of the parent function.

Step 10 ：D. It has 5 zeros and at most 4 relative maximums or minimums.