Lesson Worksheet: Function Rules Mathematics • 6th Grade

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


Find the rule for the following function table.

Input (π‘₯)12345
Output (β‹―)1014182226
  • A4π‘₯+6
  • B6π‘₯+4
  • C6π‘₯βˆ’4
  • D4π‘₯βˆ’6
  • Eπ‘₯+6


Find the rule for the given function table.

Input (π‘₯)1410
Output (β‹―)91218
  • A8π‘₯βˆ’8
  • B8βˆ’π‘₯
  • Cπ‘₯+8
  • D8π‘₯+8
  • Eπ‘₯βˆ’8


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

Input (π‘₯)1213141516
Output (𝑦)768288β‹―β‹―
  • A𝑦=7π‘₯+5, 94, 117
  • B𝑦=7π‘₯+5, 110, 100
  • C𝑦=6π‘₯+4, 94, 20
  • D𝑦=6π‘₯+4, 19, 100
  • E𝑦=6π‘₯+4, 94, 100


By using the linear relation π‘Ž+2𝑏=βˆ’8, fill in the missing values in the table.

  • A𝑏=βˆ’12, π‘Ž=52, 𝑏=8
  • B𝑏=βˆ’5, π‘Ž=βˆ’14, 𝑏=0
  • C𝑏=βˆ’12, π‘Ž=βˆ’52, 𝑏=8
  • D𝑏=βˆ’5, π‘Ž=βˆ’2, 𝑏=0
  • E𝑏=βˆ’5, π‘Ž=βˆ’12, 𝑏=0


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 𝑔 represent the number of guests and represent 𝑐 the number of sandwiches per guest.

  • A𝑐=42𝑔
  • B𝑐=42+𝑔
  • C𝑐=42βˆ’π‘”
  • D𝑐=42÷𝑔
  • E𝑐=𝑔÷42


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 𝑛 weeks overdue.

Weeks Overdue 1 2 3 𝑛
Fee ($) 9 11 13 β‹―
  • A2𝑛
  • B7𝑛+2
  • C2𝑛+7
  • D7π‘›βˆ’2
  • E2π‘›βˆ’7


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 company’s total cost.

Company A$40 per day$35 cleaning and maintenance fees
Company B2 days cost $707 days cost $280
  • ACompany A: 𝑦=35π‘₯+40, company B: 𝑦=42π‘₯βˆ’14
  • BCompany A: 𝑦=40π‘₯+35, company B: 𝑦=42π‘₯βˆ’14
  • CCompany A: 𝑦=40π‘₯+35, company B: 𝑦=βˆ’14π‘₯+42
  • DCompany A: 𝑦=140+35, company B: 𝑦=42π‘₯βˆ’14
  • ECompany A: 𝑦=40π‘₯+35, company B: π‘₯42βˆ’14


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.

  • A𝑦=20.25π‘₯βˆ’10
  • B𝑦=10π‘₯βˆ’20.25
  • C𝑦=20.25π‘₯+10
  • D𝑦=30.25π‘₯βˆ’10
  • E𝑦=10π‘₯+20.25


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: 𝑦=10π‘₯+5, rental B: 𝑦=6π‘₯+1
  • Brental A: 𝑦=10π‘₯βˆ’5, rental B: 𝑦=6π‘₯+1
  • Crental A: 𝑦=5π‘₯+10, rental B: 𝑦=16π‘₯+16
  • Drental A: 𝑦=10π‘₯+5, rental B: 𝑦=6π‘₯βˆ’1
  • Erental A: 𝑦=5π‘₯+10, rental B: 𝑦=π‘₯+6


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 pool’s total cost for π‘₯ swims.

  • Apool A: 𝑦=7π‘₯+150, pool B: 𝑦=π‘₯8+140
  • Bpool A: 𝑦=7π‘₯βˆ’150, pool B: 𝑦=8π‘₯βˆ’140
  • Cpool A: 𝑦=7π‘₯+150, pool B: 𝑦=8π‘₯+140
  • Dpool A: 𝑦=150π‘₯+7, pool B: 𝑦=140π‘₯+8
  • Epool A: 𝑦=7π‘₯βˆ’150, pool B: 𝑦=8π‘₯+140

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