$f(x)=4 x+5$, has a domain $0 \leq x \leq 50$. What is its range?

Step 1 ：The function given is \(f(x)=4 x+5\), and the domain is \(0 \leq x \leq 50\).

Step 2 ：The range of a function is the set of all possible output values (y-values) which we get after substituting all the possible x-values in the function.

Step 3 ：In this case, the function is a linear function and we can find the range by substituting the extreme values of the domain (0 and 50) in the function.

Step 4 ：Substituting \(x = 0\) in the function, we get \(f(0) = 4*0 + 5 = 5\). So, the lower limit of the range is 5.

Step 5 ：Substituting \(x = 50\) in the function, we get \(f(50) = 4*50 + 5 = 205\). So, the upper limit of the range is 205.

Step 6 ：Therefore, the range of the function \(f(x)=4 x+5\) for the domain \(0 \leq x \leq 50\) is \(\boxed{5 \leq y \leq 205}\).