Locating the Range
3. How to Actually Find the Range
Now, let's put our knowledge into practice. How do you actually find the range of a step graph when you're staring at one? Don't panic; it's a systematic process. First, you need the graph itself, either physically (on paper) or digitally (on a screen). If you only have the function's definition (the equation that makes the step function), you'll likely need to plot it to visually identify the steps.
Next, carefully examine the graph. Identify all the horizontal line segments (the steps). For each step, determine the y-value. This is the value that the function is equal to on that particular interval. Sometimes, this may be explicitly stated. Other times, you might need to read the y-value off the y-axis. Accuracy is key here!
Once you've identified the y-values for all the steps, compile them into a set. Remember, sets don't allow duplicates, so if a y-value appears on multiple steps (which is rare but possible), you only include it once in the range. This is extremely important! For example, the set {2,2,3,4} is simply {2,3,4}.
Finally, present your answer clearly. The range should be written as a set of numbers, enclosed in curly braces { }. For instance, if the y-values are 1, 3, and 5, the range would be {1, 3, 5}. You can order it from smallest to largest if you like, but it's not strictly necessary. You've officially conquered the range of a step graph! High five!
