Practical Examples of Functions Represented by Tables & Ordered Pairs

📚 Quick Study Guide

• 🔢 A function relates each input to exactly one output. Think of it as a machine: you put something in, and you always get the same thing out for the same input.
• 📝 A table represents a function by showing input-output pairs in rows or columns. Each input should have only one corresponding output.
• 📍 Ordered pairs are written as (input, output), or (x, y). A set of ordered pairs represents a function if each x-value appears only once.
• 📈 To determine if a table or set of ordered pairs represents a function, check that no input (x-value) is associated with more than one output (y-value).
• 💡 Domain is the set of all possible input values (x-values).
• 🎯 Range is the set of all possible output values (y-values).

Practice Quiz

1. Which of the following tables represents a function?

   1. x	y
      1	2
      1	3

   2. x	y
      2	4
      3	6

   3. x	y
      4	8
      4	10

   4. x	y
      5	10
      5	12

2. Which set of ordered pairs represents a function?
   1. {(1, 2), (1, 3), (2, 4)}
   2. {(3, 5), (4, 5), (5, 5)}
   3. {(6, 7), (7, 8), (6, 9)}
   4. {(8, 10), (9, 11), (8, 12)}
3. Given the table:

   x	y
   -1	1
   0	0
   1	1

   . What is the range of the function?
   1. {-1, 0, 1}
   2. {0, 1}
   3. {-1, 0}
   4. {1}
4. Which of the following ordered pairs, when added to the set {(2, 5), (3, 7), (4, 9)}, would NOT result in a function?
   1. (5, 11)
   2. (6, 13)
   3. (2, 6)
   4. (7, 15)
5. A function is represented by the following table:

   x	y
   1	a
   2	b
   3	c

   . Which statement must be true for it to be a function?
   1. a = b = c
   2. a, b, and c are all different
   3. a, b, and c can be any values
   4. Each x-value must map to a unique y-value (a, b, and c do not necessarily have to be different)
6. Consider the set of ordered pairs: {(1, a), (2, b), (3, a)}. Which of the following is true?
   1. It is not a function because 'a' is repeated.
   2. It is a function if a = b.
   3. It is a function regardless of the values of 'a' and 'b'.
   4. It is a function only if a is not equal to b.
7. Which table does NOT represent a function?

   1. x	y
      0	1
      1	2
      2	3

   2. x	y
      -1	1
      0	0
      1	1

   3. x	y
      2	4
      3	9
      2	16

   4. x	y
      -2	4
      -1	1
      0	0