Domain & Range

Functions in mathematics can be compared to the operations of a vending (soda) machine. When you put in a certain amount of money, you can select different types of sodas. Similarly, for functions, we input different numbers and we get new numbers as the result. Domain and range are the main aspects of functions. You can use quarters and one-dollar bills to buy a soda. The machine will not give you any flavor of the soda if pennies are input. Hence, the domain represents the inputs we can have here, that is, quarters and one-dollar bills. No matter what amount you pay, you won’t get a cheeseburger from a soda machine. Thus, the range is the possible outputs we can have here, that is, the flavors of soda in the machine. Let us learn to find the domain and range of a given function, and also graph them.

It’s always a lot easier to work out the domain and range when reading it off the graph (but we must make sure we zoom in and out of the graph to make sure we see everything we need to see). However, we don’t always have access to graphing software, and sketching a graph usually requires knowing about discontinuities and so on first anyway.

As mentioned earlier, the key things to check for are:

1. There are no negative values under a square root sign

2. There are no zero values in the denominator (bottom) of a fraction