Some students have difficulty determining the domain and range of a function. If you can graph the function using a graphing utility or making an x,y table and plotting points to create the graph, then seeing the domain and range is much simpler.
The domain is the set of x values, or the input of the function. The range is the output or the y-value of the function.
For example, if the function is f(x) = x^2 + 3x and the input is x = 1, the output is f(1), which is the same as y = (1)^2 + 3(1) = 4.
Looking at a graph, the amount the graph stretches horizontally is the domain and the amount the graph stretches vertically is the range.
If the function is just represented as an (x,y) table, the domain is all the x values and the range is all the y values.