Well, I cant give you all the examples of rational and radical functions, because that would be cheating but I will help you.

For you to make these functions its best to use its formula then solve it. You could make your own equation and then solve it. Maybe graph it, if it's asked.

Radical Function Formula or example of a radical function:

\(f(x) = \sqrt{x}\)

Rational Function Formula or example of a rational function:

\(f(x) = \frac{1}{x}\)

Those two formulas above are the parent roots, so the functions can get more complex.

Also f(x) does also means y

You could put any numbers in the formula to make a function. But you need to have y and x as variable. So you could add on to the parental root.

I will provide 1 example for each, as a base so that you could understand a little bit better:

Radical Function Example:

\(f(x) = \sqrt{(4-x)}\)

Rational Function Example:

\(f(x) = \frac{3}{x + 2}\)

See that you could add more if you needed to or just for your examples. I dont know what type of solution they are asking for, depends on how you would create the solution. If they are asking for intercepts, solutions for domains or ranges, or a inequality. It depends on what they are asking for. I suggest looking for websites to help with this. Im sure they provide exaples to help you. This website has a calculator if you need one or you could find one on a website of some sort. And since this is functions they could ask for graphing, a good graphing website is Desmos.

I really Hope this Helps ;P