Step 1 :The y-intercept of a function is the point where the graph of the function intersects the y-axis. This occurs when x = 0. So, to find the y-intercept of the given functions, we need to substitute x = 0 into each function and see which one gives us a y-value of 4.
Step 2 :Substitute x = 0 into each function: \(y_A = -4.0\), \(y_B = -0.25\), \(y_C = 4.0\), \(y_D = -2.0\)
Step 3 :From the results, we can see that when x = 0, only function C gives a y-value of 4.
Step 4 :Final Answer: The function with a y-intercept of 4 is \(\boxed{f(x)=\frac{x-8}{x-2}}\)