A step function is a function that includes a series of horizontal lines, which jump from one to the other at regular intervals.

• A step function graph will include open and closed dots. These open and closed dots pairs are where the function “jumps”
• The jumps will usually occur at whole number values of the x-axis

Here is an example question from the 2017 ACT:

For ABC cabs, the price of a taxi fare jumps $2 each time the fare reaches a new whole number value. This means for any distance of less than 1 whole mile, the fare is $2. As soon as 1 whole mile is reached, the price then jumps to $4. It stays at that price until 2 full miles are reached, and so on.

The prices on the Y-axis are flat fares (they are not per mile). So to compare the price of a 5-mile fare for each company, a student must simply compare the y-values at x = 5 for both companies. For a 5-mile trip, ABC will charge $12 and Tary will charge $9. Therefore, the cheaper fare is $9.