Determine which of the rational functions given below has the following feature. $y$-intercept is 4
A. $f(x)=\frac{x+8}{x-2}$
B. $f(x)=\frac{2 x-1}{x+4}$
c. $f(x)=\frac{x-8}{x-2}$
D. $f(x)=\frac{x+4}{x-2}$
Answer
Final Answer: The function with a y-intercept of 4 is \(\boxed{f(x)=\frac{x-8}{x-2}}\)
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 \(\boxed{f(x)=\frac{x-8}{x-2}}\)
