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{{ printedBook.courseTrack.name }} {{ printedBook.name }} 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,for0<x≤2502,for250<x≤5003,for500<x≤7504,for750<x≤10005,for1000<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!