Which of the following equations represents a rational function that has horizontal shift right 5 , reflection across the x-axis, vertical stretch by 14 , and vertical shift up 6 ?

f(x)={14}/{x+5}+6
f(x)=-{14}/{x-5}+6
f(x)={1}/{14(x-5)}+6
f(x)=-{1}/{14(x-5)}-6

Step 1 ：A rational function is a function that can be represented as the ratio of two polynomials. The transformations of the function can be represented in the function equation as follows:

Step 2 ：Horizontal shift right 5 is represented by \((x-5)\) in the function.

Step 3 ：Reflection across the x-axis is represented by a negative sign in front of the function.

Step 4 ：Vertical stretch by 14 is represented by multiplying the function by 14.

Step 5 ：Vertical shift up 6 is represented by adding 6 to the function.

Step 6 ：So, the function that represents these transformations is \(f(x)=-\frac{14}{x-5}+6\).

Step 7 ：Final Answer: \(\boxed{f(x)=-\frac{14}{x-5}+6}\)