# Lesson Worksheet: Function Rules Mathematics • 6th Grade

In this worksheet, we will practice finding a function rule from a given function table.

**Q3: **

Find the function rule for this table. Then calculate the two missing numbers.

Input | 12 | 13 | 14 | 15 | 16 |
---|---|---|---|---|---|

Output | 76 | 82 | 88 |

- A, 94, 117
- B, 110, 100
- C, 94, 20
- D, 19, 100
- E, 94, 100

**Q5: **

Charlotte prepared 42 sandwiches for her guests. Write a function rule that relates the number of sandwiches per guest to the number of guests. Let represent the number of guests and represent the number of sandwiches per guest.

- A
- B
- C
- D
- E

**Q6: **

The given table shows the fee for borrowed books that are overdue at a library. Determine which expression could be used to find the fee for a book that is weeks overdue.

Weeks Overdue | 1 | 2 | 3 | |
---|---|---|---|---|

Fee ($) | 9 | 11 | 13 | ? |

- A
- B
- C
- D
- E

**Q7: **

Matthew is trying to choose a car rental company. The relationship between the number of rental days and the total cost of the rental is linear for each company. Write the corresponding linear functions that describe each car rental companyβs total cost.

Company A | $40 per day | $35 cleaning and maintenance fees |
---|---|---|

Company B | 2 days cost $70 | 7 days cost $280 |

- Acompany A: , company B:
- Bcompany A: , company B:
- Ccompany A: , company B:
- Dcompany A: , company B:
- Ecompany A: , company B:

**Q8: **

At a flea market, a woman sells her homemade hacky sacks. She paid $10.00 to have a stall erected at the market and makes $20.25 for every hacky sack she sells. Write a function for the money she earns.

- A
- B
- C
- D
- E

**Q9: **

A group of friends want to go cycling and are trying to choose a bike rental company. Rental A charges $10 per hour plus a rental fee of $5, whereas rental B charges $7 for 1 hour and $25 for 4 hours. Given that the relationship between the number of hours and the cost is linear for both bike rental companies, write the corresponding linear functions that describe the total cost of each company.

- Arental A: , rental B:
- Brental A: , rental B:
- Crental A: , rental B:
- Drental A: , rental B:
- Erental A: , rental B:

**Q10: **

Hannah is trying to decide which pool to go swimming in. There are two nearby pools: pool A, which has a membership fee of $150 and charges $7 per visit, and pool B, which charges $260 for 15 visits and $316 for 22 visits. Write the corresponding linear functions that describe each poolβs total cost for swims.

- Apool A: , pool B:
- Bpool A: , pool B:
- Cpool A: , pool B:
- Dpool A: , pool B:
- Epool A: , pool B:

**Q12: **

Write a function that describes the distance Michael jogs after minutes.

Time (min) | 5 | 10 | 20 |
---|---|---|---|

Distance Jogged (mi) | 0.75 | 1.5 | 3 |

- A
- B
- C
- D
- E

**Q16: **

At Elmwood Middle School, sixth graders spend 3 hours every night studying, seventh graders spend 4 hours, eighth graders spend 5 hours. Let the studentsβ grade be the input , what is the function rule between the studentsβ grade and the amount of time the students spend on homework every night?

- A
- B
- C
- D
- E

**Q17: **

A supermarket deducts $13 off the total purchase for customers visiting between 5 am and 6 am. Find a function rule that relates the final cost to the total purchase amount. Let the total purchase amount be denoted by and the final cost by .

- A
- B
- C
- D
- E

**Q18: **

What is the mathematical relation between and for the values in the table?

Input () | 16 | 63 | 87 |
---|---|---|---|

Output () | 13 | 60 | 84 |

- A
- B
- C
- D

**Q19: **

The table shows the relationship between the number of gas canisters bought and the total cost.

Number Bought | 10 | 15 | 20 | 30 |
---|---|---|---|---|

Total Cost | $25.00 | $37.50 | $50.00 | $75.00 |

Write an equation for the total cost, , of buying gas canisters.

- A
- B
- C
- D
- E

**Q20: **

Write the equation that expresses in terms of for the numbers in the table.

0 | 1 | 2 | 3 | |

6 | 5 | 4 | 3 |

- A
- B
- C
- D
- E

**Q21: **

What is the mathematical relation between and for the values in the table?

Input () | 117 | 450 | 144 |
---|---|---|---|

Output () | 13 | 50 | 16 |

- A
- B
- C
- D

**Q22: **

The table represents a proportional relationship between and . Write an equation to describe the relationship between and .

1 | 2 | |||

1 | 2 | 3 | 4 |

- A
- B
- C
- D
- E

**Q23: **

Write the equation that expresses in terms of for the numbers in the table.

2 | 3 | 4 | 5 | |

1 | 6 | 11 | 16 |

- A
- B
- C
- D
- E

**Q24: **

Use the table to write an expression for the total cost, , of buying gas canisters.

Number Bought | 10 | 12 | 15 | 20 |
---|---|---|---|---|

Total Cost |

- A
- B
- C
- D
- E

**Q25: **

James sold glasses of lemonade during the spring and summer to raise money to buy a car. The table shows how many glasses he sold each month as well as the profit he made. Write an equation which shows the relationship between the number of glasses sold and the profit made .

March | April | May | June | July | August | September | |
---|---|---|---|---|---|---|---|

Glasses Sold | 8 | 3 | 2 | 12 | 10 | 5 | 4 |

Profit | $36.00 | $13.50 | $9.00 | $54.00 | $45.00 | $22.00 | $18.00 |

- A
- B
- C
- D
- E