Worksheet: Domains and Ranges of Relations and Functions

In this worksheet, we will practice extracting the domain and range from a given function.

Q1:

By completing the table that shows the cost, 𝑦 , of buying 𝑥 movie tickets, state the domain and range.

Number of people ( 𝑥 ) 1 2 3 4
Cost of movie tickets in dollars ( 𝑦 ) 11
  • Adomain = { 1 , 2 , 3 , 4 } , range = { 1 1 , 2 4 , 3 6 , 4 8 }
  • Bdomain = { 1 1 , 2 2 , 3 3 , 4 4 } , range = { 1 , 2 , 3 , 4 }
  • Cdomain = { 1 1 , 2 4 , 3 6 , 4 8 } , range = { 1 , 2 , 3 , 4 }
  • Ddomain = { 1 , 2 , 3 , 4 } , range = { 1 1 , 2 2 , 3 3 , 4 4 }
  • Edomain = { 1 , 2 , 3 , 4 } , range = { 2 2 , 3 3 , 4 4 , 5 5 }

Q2:

Identify the domain and range of the following function: the rule is 𝑦 = 𝑥 4 and 𝑥 { 9 , 1 0 , 1 1 , 1 2 } .

  • Adomain = { 9 , 1 0 , 1 1 , 1 2 } , range = { 1 3 , 1 4 , 1 5 , 1 6 }
  • Bdomain = { 5 , 6 , 7 , 8 } , range = { 9 , 1 0 , 1 1 , 1 2 }
  • Cdomain = { 1 3 , 1 4 , 1 5 , 1 6 } , range = { 9 , 1 0 , 1 1 , 1 2 }
  • Ddomain = { 9 , 1 0 , 1 1 , 1 2 } , range = { 5 , 6 , 7 , 8 }
  • Edomain = { 9 , 1 0 , 1 1 , 1 2 } , range = { 6 , 7 , 8 , 9 }

Q3:

Given that 𝑥 { 6 , 7 , 8 , 9 } , identify the domain and range of the function 𝑦 = 𝑥 3 . 5 .

  • Adomain = { 6 , 7 , 8 , 9 } , range = { 9 . 5 , 1 0 . 5 , 1 1 . 5 , 1 2 . 5 }
  • Bdomain = { 2 . 5 , 3 . 5 , 4 . 5 , 5 . 5 } , range = { 6 , 7 , 8 , 9 }
  • Cdomain = { 9 . 5 , 1 0 . 5 , 1 1 . 5 , 1 2 . 5 } , range = { 6 , 7 , 8 , 9 }
  • Ddomain = { 6 , 7 , 8 , 9 } , range = { 2 . 5 , 3 . 5 , 4 . 5 , 5 . 5 }
  • Edomain = { 6 , 7 , 8 , 9 } , range = { 3 . 5 , 4 . 5 , 5 . 5 , 6 . 5 }

Q4:

A cyclist leaves a town and travels at a constant speed. The table below shows the distance travelled against time. Use it to find the cyclist's speed and the distance he travelled in 630 minutes.

Distance Travelled (km) 60 120 180 240
Time (h) 3 6 9 12

  • AThe speed is 10 km/h and the distance is 210 km.
  • BThe speed is 20 km/h and the distance is 240 km.
  • CThe speed is 20 km/h and the distance is 420 km.
  • DThe speed is 20 km/h and the distance is 210 km.

Q5:

Identify the domain and range of the following function: the rule is 𝑦 = 5 𝑥 + 9 and 𝑥 { 1 , 2 , 3 , 4 } .

  • Adomain = { 1 , 2 , 3 , 4 } , range = { 1 0 , 1 1 , 1 2 , 1 3 }
  • Bdomain = { 1 4 , 1 9 , 2 4 , 2 9 } , range = { 1 , 2 , 3 , 4 }
  • Cdomain = { 1 0 , 1 1 , 1 2 , 1 3 } , range = { 1 , 2 , 3 , 4 }
  • Ddomain = { 1 , 2 , 3 , 4 } , range = { 1 4 , 1 9 , 2 4 , 2 9 }
  • Edomain = { 1 , 2 , 3 , 4 } , range = { 1 4 , 1 , 6 , 1 1 }

Q6:

What is the range of a function?

  • A the set of values that can go into the function
  • B the set of values that may possibly come out of the function
  • C the set of values that may possibly come out of or go into the function
  • Dthe outputs of a function
  • Ethe set of values that actually comes out of or goes into the function

Q7:

What is the domain of a function?

  • A the set of values that actually comes out of the function
  • B the set of values that may possibly come out of the function
  • C the set of values that may possibly come out of or go into the function
  • Dthe set of inputs of a function
  • Ethe set of values that actually comes out of or goes into the function

Q8:

True or False: Every function is a mathematical relation, but not every mathematical relation is a function.

  • ATrue
  • BFalse

Q9:

Crocodile can swim up to 10 miles per hour. Write a function rule that represents the total number of miles a crocodile can swim at this rate, using to represent the number of hours and 𝑡 to represent the total number of miles. Then, use that function rule to determine the total number of miles a crocodile can swim in five hours.

  • A 𝑡 = , 10
  • B 𝑡 = + 1 0 , 15
  • C 𝑡 = 1 0 , 5
  • D 𝑡 = 1 0 , 50
  • E 𝑡 = 1 0 , 60

Q10:

An artist bought 8 brushes for $5.00 each, and he had a coupon for $2.31 off his total purchase. Write a function rule to represent the total purchase price, letting 𝑐 represent the number of brushes and 𝑦 the total amount he spent on them, and then determine that amount.

  • A 𝑦 = 5 𝑐 2 . 3 1 , $32.69
  • B 𝑦 = 5 𝑐 + 2 . 3 1 , $42.31
  • C 𝑦 = 5 𝑐 + 2 . 3 1 , $32.69
  • D 𝑦 = 5 𝑐 2 . 3 1 , $37.69
  • E 𝑦 = 𝑐 + 2 . 6 9 , $10.69

Q11:

Amir wants to calculate the total cost for reserving a number of nights in a particular hotel. If the cost for a night is $50 plus a registration fee of $70, write a function that describes the total cost based on the number of nights. What is the initial cost for this function?

  • A 𝑦 = 7 0 𝑥 5 0 , initial cost = 5 0
  • B 𝑦 = 7 0 𝑥 + 5 0 , initial cost = 5 0
  • C 𝑦 = 5 0 𝑥 + 7 0 , initial cost = 1 2 0
  • D 𝑦 = 5 0 𝑥 + 7 0 , initial cost = 7 0
  • E 𝑦 = 5 0 𝑥 7 0 , initial cost = 7 0

Q12:

A pizza shop sells 41 pizzas each hour. By making a function table that shows the number of pizzas sold after 1, 2, 3, and 4 hours, determine the domain and range.

  • Adomain = { 1 , 2 , 3 , 4 } , range = { 4 1 , 8 4 , 1 2 6 , 1 6 8 }
  • Bdomain = { 4 1 , 8 2 , 1 2 3 , 1 6 4 } , range = { 1 , 2 , 3 , 4 }
  • Cdomain = { 4 1 , 8 4 , 1 2 6 , 1 6 8 } , range = { 1 , 2 , 3 , 4 }
  • Ddomain = { 1 , 2 , 3 , 4 } , range = { 4 1 , 8 2 , 1 2 3 , 1 6 4 }
  • Edomain = { 1 , 2 , 3 , 4 } , range = { 4 1 , 8 2 , 1 2 3 , 8 2 0 }

Q13:

A multiplayer online game charges $16 for signing up to play and then charges $9.86 monthly. Let 𝑏 represent the number of months the game is played and 𝑡 the total cost. Write a function rule to represent the total cost, and then find how much the first 3 months of playing the game would cost.

  • A 𝑡 = 9 . 8 6 𝑏 + 1 6 , $160.76
  • B 𝑡 = 9 . 8 6 × ( 𝑏 + 1 6 ) , $187.34
  • C 𝑡 = 9 . 8 6 × ( 𝑏 + 1 6 ) , $189.34
  • D 𝑡 = 9 . 8 6 𝑏 + 1 6 , $45.58
  • E 𝑡 = 𝑏 + 9 . 8 6 + 1 6 , $28.86

Q14:

Find the domain and range of the following function: the rule is 𝑦 = 3 𝑥 and 𝑥 { 7 , 8 , 9 , 1 0 } .

  • Adomain = { 7 , 8 , 9 , 1 0 } , range = { 1 0 , 1 1 , 1 2 , 1 3 }
  • Bdomain = { 2 1 , 2 4 , 2 7 , 3 0 } , range = { 7 , 8 , 9 , 1 0 }
  • Cdomain = { 1 0 , 1 1 , 1 2 , 1 3 } , range = { 7 , 8 , 9 , 1 0 }
  • Ddomain = { 7 , 8 , 9 , 1 0 } , range = { 2 1 , 2 4 , 2 7 , 3 0 }
  • Edomain = { 7 , 8 , 9 , 1 0 } , range = { 2 4 , 2 7 , 3 0 , 3 3 }

Q15:

A projectile is released from a point on a flat plane. The height of the projectile can be calculated, at a given time , using the function . Given that the projectile can NOT travel beneath the surface of the plane, work out the domain of the function.

  • A
  • B
  • C
  • D
  • E

Q16:

The function 𝑓 is defined by

Solve 𝑓 ( 𝑥 ) = 2 6 for 𝑥 .

  • A 𝑥 = 3
  • B 𝑥 = 1
  • C 𝑥 = 4
  • D 𝑥 = 2
  • E 𝑥 = 5

Q17:

Use the following graph of the function 𝑓 to solve 𝑓 ( 𝑥 ) = 1 4 .

  • A 𝑥 = 3
  • B 𝑥 = 6
  • C 𝑥 = 4
  • D This has no solution.
  • E 𝑥 = 5

Q18:

Use the following table to solve 𝑓 ( 𝑥 ) = 2 6

𝑥 1 2 3 4 5 6
𝑓 ( 𝑥 ) 3 1 2 6 1 9 1 0 1 14
  • A 𝑥 = 3
  • B 𝑥 = 1
  • C 𝑥 = 4
  • D 𝑥 = 2
  • E 𝑥 = 5

Q19:

Identify the domain and range of the following function: the rule is 𝑦 = 𝑥 + 4 and 𝑥 { 8 , 9 , 1 0 , 1 1 } .

  • Adomain = { 8 , 9 , 1 0 , 1 1 } , range = { 4 , 5 , 6 , 7 }
  • Bdomain = { 1 2 , 1 3 , 1 4 , 1 5 } , range = { 8 , 9 , 1 0 , 1 1 }
  • Cdomain = { 4 , 5 , 6 , 7 } , range = { 8 , 9 , 1 0 , 1 1 }
  • Ddomain = { 8 , 9 , 1 0 , 1 1 } , range = { 1 2 , 1 3 , 1 4 , 1 5 }
  • Edomain = { 8 , 9 , 1 0 , 1 1 } , range = { 1 3 , 1 4 , 1 5 , 1 6 }

Q20:

Given that 𝑥 { 3 , 4 , 5 , 6 } , identify the domain and range of the function 𝑦 = 𝑥 + 0 . 2 5 .

  • Adomain = { 3 , 4 , 5 , 6 } , range = { 2 . 7 5 , 3 . 7 5 , 4 . 7 5 , 5 . 7 5 }
  • Bdomain = { 3 . 2 5 , 4 . 2 5 , 5 . 2 5 , 6 . 2 5 } , range = { 3 , 4 , 5 , 6 }
  • Cdomain = { 2 . 7 5 , 3 . 7 5 , 4 . 7 5 , 5 . 7 5 } , range = { 3 , 4 , 5 , 6 }
  • Ddomain = { 3 , 4 , 5 , 6 } , range = { 3 . 2 5 , 4 . 2 5 , 5 . 2 5 , 6 . 2 5 }
  • Edomain = { 3 , 4 , 5 , 6 } , range = { 4 . 2 5 , 5 . 2 5 , 6 . 2 5 , 7 . 2 5 }

Q21:

Identify the domain and range of the following function: the rule is 𝑦 = 7 𝑥 2 and 𝑥 { 7 , 8 , 9 , 1 0 } .

  • Adomain = { 7 , 8 , 9 , 1 0 } , range = { 5 1 , 5 8 , 6 5 , 7 2 }
  • Bdomain = { 4 7 , 5 4 , 6 1 , 6 8 } , range = { 7 , 8 , 9 , 1 0 }
  • Cdomain = { 5 1 , 5 8 , 6 5 , 7 2 } , range = { 7 , 8 , 9 , 1 0 }
  • Ddomain = { 7 , 8 , 9 , 1 0 } , range = { 4 7 , 5 4 , 6 1 , 6 8 }
  • Edomain = { 7 , 8 , 9 , 1 0 } , range = { 5 4 , 6 1 , 6 8 , 7 5 }

Q22:

Crocodile can swim up to 10 miles per hour. Write a function rule that represents the total number of miles a crocodile can swim at this rate, using to represent the number of hours and 𝑡 to represent the total number of miles. Then, use that function rule to determine the total number of miles a crocodile can swim in three hours.

  • A 𝑡 = , 10
  • B 𝑡 = + 1 0 , 13
  • C 𝑡 = 1 0 , 7
  • D 𝑡 = 1 0 , 30
  • E 𝑡 = 1 0 , 40

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