Question

a relation is defined by the function y = z +2, where z is a member of { 1,2,3,}
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 \(\{(1, 3), (2, 4), (3, 5)\}\).