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Worksheet: Writing an Equation to Represent a Function

Q1:

The membership of a music club costs $15 per month, as shown in the table. Write an equation for the total cost, 𝑑 , of a music club membership for a duration of 𝑑 months.

Number of Months, 𝑑 1 2 3 4
Cost, 𝑑 15 30 45 60
  • A 𝑑 = 1 5 + 𝑑
  • B 𝑑 = 1 5 𝑑
  • C 𝑑 = 1 5 + 𝑑
  • D 𝑑 = 1 5 𝑑
  • E 𝑑 = 1 5 βˆ’ 𝑑

Q2:

A portion of fencing 100 feet long is cut into two pieces. One piece, which is π‘₯ feet long, is used to enclose a square pen. The other piece is shaped into an enclosure as an equilateral triangle. What is the total area enclosed as a function of π‘₯ ?

  • A 𝐴 ( π‘₯ ) = ο€» π‘₯ 4  + 1 2 ο€Ό 1 0 0 βˆ’ π‘₯ 3  ο€Ό 1 0 0 βˆ’ π‘₯ 3  
  • B 𝐴 ( π‘₯ ) = π‘₯ + ( 1 0 0 βˆ’ 4 π‘₯ ) √ 3 
  • C 𝐴 ( π‘₯ ) = ο€Ύ π‘₯ 4  + ( 1 0 0 βˆ’ π‘₯ ) 6 √ 3  
  • D 𝐴 ( π‘₯ ) = π‘₯ 1 6 + ( 1 0 0 βˆ’ π‘₯ ) √ 3 3 6  

Q3:

Write an equation that describes the relationship between the input and output.

Input ( π‘₯ ) 0 2 6
Output ( 𝑦 ) 0 6 18
  • A 𝑦 = π‘₯ βˆ’ 3
  • B 𝑦 = π‘₯ + 3
  • C 𝑦 = 3 π‘₯ + 3
  • D 𝑦 = 3 π‘₯
  • E 𝑦 = 5 π‘₯

Q4:

Write an equation that describes the relationship between the input and output.

Input ( π‘₯ ) 9 15 30
Output ( 𝑦 ) 3 5 10
  • A 𝑦 = 1 3 π‘₯ + 3
  • B 𝑦 = 3 π‘₯
  • C 𝑦 = 3 π‘₯ + 3
  • D 𝑦 = 1 3 π‘₯
  • E 𝑦 = π‘₯ + 3

Q5:

Write an equation that describes the relationship between the input and output.

Input ( π‘₯ ) 1 3 8
Output ( 𝑦 ) 4 12 32
  • A 𝑦 = π‘₯ βˆ’ 4
  • B 𝑦 = π‘₯ + 4
  • C 𝑦 = 4 π‘₯ + 4
  • D 𝑦 = 4 π‘₯
  • E 𝑦 = 7 π‘₯

Q6:

Amelia is going biking. For every mile she bikes, she burns 125 calories. In the graph and table below, 𝑛 represents the number of miles she bikes, and 𝑐 represents the number of calories she burns. Write an equation for the number of calories, 𝑐 , that she burns if she bikes 𝑛 miles.

𝑛 1 2 3 4
𝑐 125 250 375 500
  • A 𝑐 = 1 2 5 + 𝑛
  • B 𝑐 = 1 1 2 5 𝑛
  • C 𝑐 = 𝑛 βˆ’ 1 2 5
  • D 𝑐 = 1 2 5 𝑛
  • E 𝑐 = 2 5 0 𝑛

Q7:

Find an equation that represents the function in the table.

Input, π‘₯ 2 20 24 36
Output, 𝑦 2 11 13 19
  • A 𝑦 = π‘₯ βˆ’ 1
  • B 𝑦 = π‘₯ 2 βˆ’ 1
  • C 𝑦 = π‘₯ + 1
  • D 𝑦 = π‘₯ 2 + 1
  • E 𝑦 = π‘₯ 2 βˆ’ 2

Q8:

Find an equation that represents the function in the table.

Input, π‘₯ 8 10 26 36
Output, 𝑦 2 3 11 16
  • A 𝑦 = π‘₯ βˆ’ 2
  • B 𝑦 = π‘₯ 2 + 2
  • C 𝑦 = π‘₯ + 2
  • D 𝑦 = π‘₯ 2 βˆ’ 2

Q9:

Find an equation that represents the function in the table.

Input, π‘₯ 6 8 14 36
Output, 𝑦 6 7 10 21
  • A 𝑦 = π‘₯ βˆ’ 3
  • B 𝑦 = π‘₯ 2 βˆ’ 3
  • C 𝑦 = π‘₯ + 3
  • D 𝑦 = π‘₯ 2 + 3
  • E 𝑦 = π‘₯ 3 βˆ’ 2

Q10:

If 𝑃 is the perimeter of a square whose side length is 𝑙 , determine 𝑃 as a function of 𝑙 , then find 𝑃 ( 1 9 ) .

  • A 𝑃 ( 𝑙 ) = 𝑙 2 , 𝑃 ( 1 9 ) = 3 6 1
  • B 𝑃 ( 𝑙 ) = 1 9 , 𝑃 ( 1 9 ) = 1 9
  • C 𝑃 ( 𝑙 ) = 𝑝 𝑙 , 𝑃 ( 1 9 ) = 1 9 𝑝
  • D 𝑃 ( 𝑙 ) = 4 𝑙 , 𝑃 ( 1 9 ) = 7 6
  • E 𝑃 ( 𝑙 ) = 𝑙 , 𝑃 ( 1 9 ) = 1 9