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 = π‘₯ βˆ’ 7
  • B 𝑦 = 7 π‘₯
  • C 𝑦 = 3 π‘₯ + 1 0
  • D 𝑦 = π‘₯ + 7
  • E 𝑦 = 3 π‘₯ βˆ’ 1 0

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$16, $64, $96
  • B$16, $24, $40
  • C $ 8 , $48, $136
  • D$8, $32, $48
  • E$8, $48, $88

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

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‘₯ Γ· 3
  • D 𝑦 = π‘₯ βˆ’ 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 = 2 5 𝑁
  • C 𝑇 = 1 0 𝑁
  • D 𝑇 = 5 2 𝑁
  • E 𝑇 = 1 5 4 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‘₯ βˆ’ 6
  • B 𝑦 = π‘₯ + 6
  • C 𝑦 = βˆ’ π‘₯ + 5
  • D 𝑦 = βˆ’ π‘₯ + 6
  • E 𝑦 = 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‘₯ + 9
  • B 𝑦 = 9 π‘₯
  • C 𝑦 = π‘₯ βˆ’ 9
  • D 𝑦 = π‘₯ Γ· 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 𝑦 = 3 π‘₯
  • B π‘₯ = 2 𝑦
  • C π‘₯ = 3 𝑦
  • D 𝑦 = 2 π‘₯
  • E 𝑦 = π‘₯ + 2

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 = π‘₯ βˆ’ 1
  • B 𝑦 = 2 π‘₯ + 1
  • C 𝑦 = 3 π‘₯ + 1
  • D 𝑦 = 5 π‘₯ βˆ’ 9
  • E 𝑦 = 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 = 2 5 . 0 0 𝑁
  • B 𝑇 = 0 . 4 0 𝑁
  • C 𝑇 = 1 0 . 0 0 𝑁
  • D 𝑇 = 2 . 5 0 𝑁
  • E 𝑇 = 3 . 7 5 𝑁

Q12:

Ramy 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

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’ π‘₯ βˆ’ 4
  • B 𝑦 = 2 π‘₯ βˆ’ 4
  • C 𝑦 = π‘₯ + 4
  • D 𝑦 = βˆ’ 2 π‘₯ + 4
  • E 𝑦 = βˆ’ 2 ( 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 π‘š = 4 𝑛 βˆ’ 1
  • C π‘š = 𝑛 βˆ’ 4
  • D 𝑛 = 4 π‘š 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 , $31
  • B π‘š = 1 9 𝑐 , $228
  • C 𝑐 = 1 9 + π‘š , $31
  • D 𝑐 = 1 9 π‘š , $228
  • E π‘š = 3 8 𝑐 , $456

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 = 2 π‘₯ βˆ’ 5
  • B 𝑦 = π‘₯ + 5
  • C 𝑦 = 2 π‘₯ βˆ’ 7
  • D 𝑦 = 2 π‘₯ + 5
  • E 𝑦 = 2 π‘₯ + 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 = π‘₯ + 3
  • B 𝑦 = 3 π‘₯ + 3
  • C 𝑦 = βˆ’ π‘₯ + 3
  • D 𝑦 = βˆ’ 3 π‘₯ + 3
  • E 𝑦 = βˆ’ 3 π‘₯ βˆ’ 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 .
  • BAdd 2 to π‘₯ to find 𝑦 .
  • CSubtract 2 from π‘₯ to find 𝑦 .
  • DMultiply π‘₯ by 4 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
  • A36, 10, 66, 14
  • B22, 10, 52, 14
  • C50, 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 less than π‘₯ .
  • BEach value of 𝑦 is 10 times greater 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 divided by 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‘₯ + 7
  • B 𝑦 = 3 π‘₯
  • C 𝑦 = 8 π‘₯ βˆ’ 5
  • D 𝑦 = 4 π‘₯ βˆ’ 1
  • E 𝑦 = 8 π‘₯ + 1 3

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?

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