Yes they are entirely contained
A rational number is a number that can be written as a fraction or "ratio".
It includes the set of integers because all of them have a denominator of 1. A rational number can take on the form of

where b ≠ 0. Terminating and repeating decimals are rational numbers because they too can be written as a ratio; for example, 0.3 =

or 0.3333... =

.
A linear function is a function with the form f(x) = ax' + b. It looks like a regular linear equation, but instead of using y, the linear function notation is f(x). To solve a linear function, you would be given the value of f(x) and be asked to find x.