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