Worksheet: Completing Function Tables and Finding Function Rules

In this worksheet, we will practice organizing input and output values in a function table and finding the function rule.

Q1:

Write the equation that expresses 𝑦 in terms of π‘₯ for the numbers in the table.

π‘₯ 0 1 2 3
𝑦 7 8 9 10
  • A 𝑦 = 3 π‘₯ βˆ’ 1 0
  • B 𝑦 = 7 π‘₯
  • C 𝑦 = 3 π‘₯ + 1 0
  • D 𝑦 = π‘₯ βˆ’ 7
  • E 𝑦 = π‘₯ + 7

Q2:

At an amusement park, a group of children decided to ride the boomerang ride. It cost $ 8 for one ticket. The table shows how the total price of the tickets depends on the number of passengers. Find the missing values in the table.

Number of Passengers 1 2 3 4 5 6
Price of Tickets $ 1 6 $ 2 4 $ 4 0
  • A$8, $32, $48
  • B$16, $64, $96
  • C$8, $48, $88
  • D$16, $24, $40
  • E $ 8 , $48, $136

Q3:

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

  • A 𝑑 = 3 ( π‘₯ βˆ’ 1 )
  • B 𝑑 = π‘₯ + 3
  • C 𝑑 = 3 π‘₯
  • D 𝑑 = π‘₯ βˆ’ 3
  • E 𝑑 = 3 ( π‘₯ + 1 )

Q4:

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 𝑝 and the final cost by 𝑐 .

  • A 𝑐 = 1 3 𝑝 βˆ’ 1 3
  • B 𝑐 = 𝑝 1 3
  • C 𝑐 = 𝑝 βˆ’ 1 3
  • D 𝑐 = 𝑝 + 1 3
  • E 𝑐 = 1 3 𝑝

Q5:

What is the mathematical relation between 𝑦 and π‘₯ for the values in the table?

Input ( π‘₯ ) 16 63 87
Output ( 𝑦 ) 13 60 84
  • A 𝑦 = π‘₯ + 3
  • B 𝑦 = 3 π‘₯
  • C 𝑦 = π‘₯ βˆ’ 3
  • D 𝑦 = π‘₯ Γ· 3

Q6:

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, 𝑇 , of buying 𝑁 gas canisters.

  • A 𝑇 = 2 5 𝑁
  • B 𝑇 = 1 5 4 𝑁
  • C 𝑇 = 1 0 𝑁
  • D 𝑇 = 2 5 𝑁
  • E 𝑇 = 5 2 𝑁

Q7:

Write the equation that expresses 𝑦 in terms of π‘₯ for the numbers in the table.

π‘₯ 0 1 2 3
𝑦 6 5 4 3
  • A 𝑦 = π‘₯ + 5
  • B 𝑦 = βˆ’ π‘₯ + 6
  • C 𝑦 = π‘₯ + 6
  • D 𝑦 = π‘₯ βˆ’ 6
  • E 𝑦 = βˆ’ π‘₯ + 5

Q8:

What is the mathematical relation between 𝑦 and π‘₯ for the values in the table?

Input ( π‘₯ ) 117 450 144
Output ( 𝑦 ) 13 50 16
  • A 𝑦 = π‘₯ Γ· 9
  • B 𝑦 = π‘₯ βˆ’ 9
  • C 𝑦 = 9 π‘₯
  • D 𝑦 = π‘₯ + 9

Q9:

The table represents a proportional relationship between π‘₯ and 𝑦 . Write an equation to describe the relationship between π‘₯ and 𝑦 .

π‘₯ 1 2 1 3 2 2
𝑦 1 2 3 4
  • A π‘₯ = 3 𝑦
  • B 𝑦 = π‘₯ + 2
  • C 𝑦 = 2 π‘₯
  • D π‘₯ = 2 𝑦
  • E 𝑦 = 3 π‘₯

Q10:

Write the equation that expresses 𝑦 in terms of π‘₯ for the numbers in the table.

π‘₯ 2 3 4 5
𝑦 1 6 11 16
  • A 𝑦 = 2 π‘₯ + 1
  • B 𝑦 = π‘₯ + 1
  • C 𝑦 = π‘₯ βˆ’ 1
  • D 𝑦 = 5 π‘₯ βˆ’ 9
  • E 𝑦 = 3 π‘₯ + 1

Q11:

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

Number Bought 10 12 15 20
Total Cost $ 2 5 . 0 0 $ 3 0 . 0 0 $ 3 7 . 5 0 $ 5 0 . 0 0
  • A 𝑇 = 0 . 4 0 𝑁
  • B 𝑇 = 1 0 . 0 0 𝑁
  • C 𝑇 = 3 . 7 5 𝑁
  • D 𝑇 = 2 . 5 0 𝑁
  • E 𝑇 = 2 5 . 0 0 𝑁

Q12:

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 ( 𝑛 ) and the profit made ( 𝑝 ) .

March April May June July August September
Glasses Sold ( 𝑛 ) 8 3 2 12 10 5 4
Profit ( 𝑝 ) $36.00 $13.50 $9.00 $54.00 $45.00 $22.00 $18.00
  • A 𝑝 = 1 3 . 5 𝑛
  • B 𝑛 = 4 . 5 𝑝
  • C 𝑝 = 9 𝑛
  • D 𝑛 = 1 3 . 5 𝑝
  • E 𝑝 = 4 . 5 𝑛

Q13:

Write the equation that expresses 𝑦 in terms of π‘₯ for the numbers in the table.

π‘₯ 5 6 7 8
𝑦 βˆ’ 6 βˆ’ 8 βˆ’ 1 0 βˆ’ 1 2
  • A 𝑦 = βˆ’ 2 π‘₯ + 4
  • B 𝑦 = 2 π‘₯ βˆ’ 4
  • C 𝑦 = βˆ’ π‘₯ βˆ’ 4
  • D 𝑦 = βˆ’ 2 ( π‘₯ + 4 )
  • E 𝑦 = π‘₯ + 4

Q14:

The table represents a linear relationship between π‘š and 𝑛 . Write an equation to describe the relationship between π‘š and 𝑛 .

π‘š 0 1 2 3
𝑛 βˆ’ 1 3 7 11
  • A 𝑛 = π‘š βˆ’ 4
  • B 𝑛 = 4 π‘š βˆ’ 1
  • C π‘š = 𝑛 βˆ’ 4
  • D π‘š = 4 𝑛 βˆ’ 1
  • E 𝑛 = 4 π‘š + 1

Q15:

The table shows the gym membership charges according to the number of months of subscription. Write an equation that represents the cost of subscription, and then determine how much a subscription for 12 months would cost.

Number of Months, π‘š 1 2 3
Cost, 𝑐 $19 $38 $57
  • A π‘š = 1 9 𝑐 , $228
  • B 𝑐 = 1 9 π‘š , $228
  • C π‘š = 3 8 𝑐 , $456
  • D π‘š = 1 9 + 𝑐 , $31
  • E 𝑐 = 1 9 + π‘š , $31

Q16:

Write the equation that expresses 𝑦 in terms of π‘₯ for the numbers in the table.

π‘₯ 0 1 2 3
𝑦 5 7 9 11
  • A 𝑦 = π‘₯ + 5
  • B 𝑦 = 2 π‘₯ + 5
  • C 𝑦 = 2 π‘₯ + 7
  • D 𝑦 = 2 π‘₯ βˆ’ 5
  • E 𝑦 = 2 π‘₯ βˆ’ 7

Q17:

Write the equation that expresses 𝑦 in terms of π‘₯ for the numbers in the table.

π‘₯ 0 1 2 3
𝑦 3 0 βˆ’ 3 βˆ’ 6
  • A 𝑦 = βˆ’ 3 π‘₯ + 3
  • B 𝑦 = 3 π‘₯ + 3
  • C 𝑦 = βˆ’ π‘₯ + 3
  • D 𝑦 = βˆ’ 3 π‘₯ βˆ’ 3
  • E 𝑦 = π‘₯ + 3

Q18:

The table shows the relationship between π‘₯ and 𝑦 . Which statement correctly describes the relationship?

π‘₯ 2 4 8 10
𝑦 8 16 32 40
  • ADivide π‘₯ by 4 to find 𝑦 .
  • BSubtract 2 from π‘₯ to find 𝑦 .
  • CMultiply π‘₯ by 4 to find 𝑦 .
  • DAdd 2 to π‘₯ to find 𝑦 .
  • EDouble 𝑦 to find π‘₯ .

Q19:

The owner of a factory calculates the daily wage of a worker according to the mathematical relation 𝑦 = 1 4 + 6 π‘₯ where 𝑦 is the daily wage in LE and π‘₯ is the number of overtime hours worked that day. Use the mathematical relation to complete the table below.

Number of Overtime Hours 6 11
Total Daily Wage 74 98
  • A50, 10, 66, 14
  • B22, 10, 52, 14
  • C36, 10, 66, 14
  • D50, 10, 80, 14

Q20:

The table shows the relationship between π‘₯ and 𝑦 . Which statement correctly describes the relationship?

π‘₯ 2 4 8 10
𝑦 12 14 18 20
  • AEach value of 𝑦 is 10 divided by π‘₯ .
  • BEach value of 𝑦 is 10 less than π‘₯ .
  • CEach value of 𝑦 is 10 times less than π‘₯ .
  • DEach value of 𝑦 is 10 greater than π‘₯ .
  • EEach value of 𝑦 is 10 times greater than π‘₯ .

Q21:

Find the function rule for the following input-output table:

Input π‘₯ 1 3 5 8 11
Output 𝑦 3 11 19 31 43
  • A 𝑦 = 4 π‘₯ βˆ’ 1
  • B 𝑦 = 8 π‘₯ + 1 3
  • C 𝑦 = 8 π‘₯ βˆ’ 5
  • D 𝑦 = 4 π‘₯ + 7
  • E 𝑦 = 3 π‘₯

Q22:

Use the rule to find the missing number in this input-output table.

Rule: 3 Γ— 𝑛 βˆ’ 7

In ( 𝑛 ) 4 5 6 7
Out ( 3 Γ— 𝑛 βˆ’ 7 ) 5 8 14

Q23:

The rule for the function machine is 4 Γ— 𝑛 βˆ’ 2 . What is the output when the input is 9?

Q24:

Which of the following equations describes the data in the given table?

π‘₯ βˆ’ 4 βˆ’ 3 βˆ’ 2 0 1
𝑦 22 15 10 6 7
  • A π‘₯ + 6 = 𝑦 
  • B π‘₯ + 6 = 𝑦
  • C 6 π‘₯ + 6 = 𝑦
  • D π‘₯ 𝑦 = 7
  • E 2 π‘₯ + 5 = 𝑦 

Q25:

Find a linear ( 𝑦 = π‘š π‘₯ + 𝑐 ) , quadratic ( 𝑦 = π‘Ž π‘₯ )  , or exponential 𝑦 = π‘Ž 𝑏  equation that fits the data in the given table.

π‘₯ βˆ’ 1 0 1 2 3
𝑦 βˆ’ 2 0 βˆ’ 2 βˆ’ 8 βˆ’ 1 8
  • A 𝑦 = βˆ’ 2 π‘₯ 
  • B 𝑦 = π‘₯ 2 
  • C 𝑦 = 2 π‘₯ 
  • D 𝑦 = 2 π‘₯ + 3
  • E 𝑦 = 2 

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