Worksheet: Writing an Equation to Represent a Function

In this worksheet, we will practice deriving equations for functions using tables and applying this in real-life situations.

Q1:

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‘₯

Q2:

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

Q3:

A right circular cone has a radius of 3 π‘₯ + 6 and its height is 3 units less than its radius. Express the volume of the cone as a polynomial function, knowing that the volume of a cone with radius π‘Ÿ and height β„Ž is 𝑉 = 1 3 πœ‹ π‘Ÿ β„Ž 2 .

  • A 𝑉 ( π‘₯ ) = πœ‹ ο€Ή 9 π‘₯ + 4 5 π‘₯ + 3 6 π‘₯ + 3 6  3 2
  • B 𝑉 ( π‘₯ ) = πœ‹ ο€Ή 9 π‘₯ + 3 6 π‘₯ + 7 2 π‘₯ + 3 6  3 2
  • C 𝑉 ( π‘₯ ) = πœ‹ ο€Ή 3 π‘₯ + 9 π‘₯ + 6  2
  • D 𝑉 ( π‘₯ ) = πœ‹ ο€Ή 9 π‘₯ + 4 5 π‘₯ + 7 2 π‘₯ + 3 6  3 2
  • E 𝑉 ( π‘₯ ) = πœ‹ ο€Ή π‘₯ + 3 π‘₯ + 2  2

Q4:

An open box is to be constructed from a piece of cardboard 8 inches by 8 inches by cutting squares from each corner and then folding up the sides. Given that the removed squares have a side length of π‘₯ inches, express the volume of the box in terms of π‘₯ as a polynomial in standard form.

  • A 𝑉 ( π‘₯ ) = 4 π‘₯ + 3 2 π‘₯ + 6 4 π‘₯ 3 2
  • B 𝑉 ( π‘₯ ) = 4 π‘₯ βˆ’ 3 2 π‘₯ + 6 4 2
  • C 𝑉 ( π‘₯ ) = 4 π‘₯ + 3 2 π‘₯ + 6 4 2
  • D 𝑉 ( π‘₯ ) = 4 π‘₯ βˆ’ 3 2 π‘₯ + 6 4 π‘₯ 3 2
  • E 𝑉 ( π‘₯ ) = 4 π‘₯ βˆ’ 3 2 π‘₯ + 1 6 π‘₯ 3 2

Q5:

A rectangle has a length of 10 units and a width of 8 units. Squares of π‘₯ by π‘₯ units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a polynomial function in terms of π‘₯ .

  • A 𝑉 ( π‘₯ ) = π‘₯ βˆ’ 1 8 π‘₯ + 8 0 π‘₯ 3 2
  • B 𝑉 ( π‘₯ ) = 4 π‘₯ + 3 6 π‘₯ + 8 0 π‘₯ 3 2
  • C 𝑉 ( π‘₯ ) = 4 π‘₯ + 4 π‘₯ + 8 0 π‘₯ 3 2
  • D 𝑉 ( π‘₯ ) = 4 π‘₯ βˆ’ 3 6 π‘₯ + 8 0 π‘₯ 3 2
  • E 𝑉 ( π‘₯ ) = 4 π‘₯ βˆ’ 4 π‘₯ + 8 0 π‘₯ 3 2

Q6:

Yasmine spends $3.88 every day on transportation to and from work. Write a function rule that relates the total amount of money Yasmine spends on transportation to the number of Yasmine’s working days. Let represent the number of Yasmine’s working days and the total amount of money she spends on transportation.

  • A
  • B
  • C
  • D
  • E

Q7:

Adel is 9 years older than Nader. Find a function rule that relates Adel’s age to Nader’s age. Let Nader’s age be denoted by and Adel’s age by .

  • A
  • B
  • C
  • D
  • E

Q8:

A cylinder has a radius of π‘₯ + 2 units and its height is 3 units greater than its radius. Express the volume of the cylinder in the form πœ‹ ( π‘ž ( π‘₯ ) ) , where π‘ž ( π‘₯ ) is a polynomial in standard form.

  • A πœ‹ ο€Ή π‘₯ + 9 π‘₯ + 2 0 π‘₯ + 2 0  3 2
  • B πœ‹ ο€Ή π‘₯ + 4 π‘₯ + 2 4 π‘₯ + 2 0  3 2
  • C πœ‹ ο€Ή 3 π‘₯ + 1 2 π‘₯ + 1 2  2
  • D πœ‹ ο€Ή π‘₯ + 9 π‘₯ + 2 4 π‘₯ + 2 0  3 2
  • E πœ‹ ο€Ή π‘₯ + 4 π‘₯ + 4  2

Q9:

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

Q10:

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

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