Remember, the domain is the list of numbers that you are allowed to place into the equation and still get a valid answer. In math terms: it is the set of numbers for your independent variable.
Your function M(h) is basically your y and your h is basically your x. So you can think about this as
y = 5x if you want. x is how many hours you work and y is the amount of money you make.
In the equation y = 5x, one variable is dependent upon the other. If you know a number for x, then you can quickly get the number for y. Therefore x is independent and y is dependent.
So in a nutshell, you are looking for all the numbers that x can be to make this valid. Since this is a real world problem(babysitting), Can you babysit negative hours? Not unless you can go back in time! So we know that negative numbers will not be in your list. Can you babysit 0 hours and make $0. Yes, it is possible. Can you babysit 1,2,3...hours, yes definitely. Can you babysit part of an hour? Like 3.2 hours or 3/4 hours? I would say yes to that.
So you can have 0, and positive nice numbers, as well as positive decimals/fractions. What set (list) of numbers is this?
Rationals: ...-4.2,-3.11, -1/2, 0, 3/4, 1.8, 3.33333333, .... (these are just examples)
Irrationals: root 2, root 3, pi (also just examples)
Things to note: you can be more specific by saying positive or negative first, like negative integers, or positive rationals or others
Also, irrationals are numbers that cannot be written as a fraction. If they cannot be written as a fraction, a a babysitter charges by the hour or part of an hour(fraction) then I do not think your answer can be irrational. I'll let you finalize your answer from the info I gave you.