If we sum up the information, we can conclude that the capacity of the theater is 250 students. This means that the drama club should do 1 performance for each group of 250 students. Let's write a pattern if x is the number of students and y=f(x) is the number of performances.
x | y=f(x) |
---|---|
0<x≤250 | 1 |
250<x≤500 | 2 |
500<x≤750 | 3 |
750<x≤1000 | 4 |
1000<x≤1250 | 5 |
The function we wrote pairs every number in each interval with the single value. Therefore, it is a step function. f(x)=⎩⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎧1, for 0<x≤2502, for 250<x≤5003, for 500<x≤7504, for 750<x≤10005, for 1000<x≤1250 Each piece of its graph will be horizontal line that is missing its left endpoint. We will show the left endpoints by open points and the right endpoints by a closed points. Let's graph it!