The following question is about the rational function \[ r(x)=\frac{(x+1)(x-3)}{(x+3)(x-4)} \] The function $r$ has $y$-intercept

Step 1 ：The problem is about the rational function \(r(x)=\frac{(x+1)(x-3)}{(x+3)(x-4)}\).

Step 2 ：We are asked to find the y-intercept of the function \(r(x)\).

Step 3 ：The y-intercept of a function is the value of the function when \(x = 0\).

Step 4 ：Substitute \(x = 0\) into the function \(r(x)\).

Step 5 ：The y-intercept of the function \(r(x)\) is \(\frac{1}{4}\).

Step 6 ：\(\boxed{\frac{1}{4}}\) is the final answer.