a relation is defined by the function y = z +2, where z is a member of { 1,2,3,}

Question

1. find the range
2.express this relation as a set of ordered pairs

Answer 1

Let's analyze the function defined by \( y = z + 2 \), where \( z \) is a member of the set \({1, 2, 3}\).

1. Finding the Range: To find the range, we can substitute each member of the set for \( z \):

   • For \( z = 1 \):
     \[ y = 1 + 2 = 3 \]
   • For \( z = 2 \):
     \[ y = 2 + 2 = 4 \]
   • For \( z = 3 \):
     \[ y = 3 + 2 = 5 \]

   The possible values of \( y \) (the output) are 3, 4, and 5. Thus, the range of the function is:

   \[ \text{Range} = {3, 4, 5} \]

2. Expressing the Relation as a Set of Ordered Pairs: We can express the relation as a set of ordered pairs \((z, y)\) for each member of the set \({1, 2, 3}\):

   • For \( z = 1 \): \((1, 3)\)
   • For \( z = 2 \): \((2, 4)\)
   • For \( z = 3 \): \((3, 5)\)

   Thus, the relation can be expressed as:

   \[ {(1, 3), (2, 4), (3, 5)} \]

In summary:

• The range is \({3, 4, 5}\).
• The relation as a set of ordered pairs is \({(1, 3), (2, 4), (3, 5)}\).