Question

algebra 1 〉 m.1 relations: convert between tables, graphs, mappings, and lists of points rbg
express the relation below as a set of ordered pairs.
domain
1
4
5
15
range
0
1
4
6
fill in all the blanks.
(□, 1)
(5, 6)
( , 4)
( , 0)

Explanation:

Step1: Analyze the mapping

In a relation, an ordered pair is \((\text{domain element}, \text{range element})\) based on the arrows. Let's check each arrow:

• Arrow from 1: Let's see where 1 maps. Wait, the arrow from 4 goes to 1? Wait, no, let's look again. Wait, the domain is {1,4,5,15}, range {0,1,4,6}. Let's track each domain element:
• Domain 4: arrow to range 1? Wait, no, the arrow from 4 to 1? Wait, the first blank is \((\square, 1)\), so we need the domain element that maps to 1. Looking at the mapping, the arrow from 4 points to 1? Wait, no, maybe I misread. Wait, the domain has 1,4,5,15. Let's check each:
• For the ordered pair \((x, 1)\): Which domain element maps to 1? Looking at the arrows, the arrow from 4 (domain) to 1 (range)? Wait, no, maybe the arrow from 1 to 0? Wait, no, let's list all mappings:
• Let's see the arrows:
• 1 maps to... Wait, the arrow from 1: let's see the lines. Wait, the domain 1 has an arrow to range 0? No, wait the cross arrows. Wait, maybe:
• Domain 4: arrow to range 1? Wait, the first blank is \((\square, 1)\), so x such that x maps to 1. So if the arrow from 4 (domain) goes to 1 (range), then \((4,1)\)? Wait, no, wait the second ordered pair is (5,6), which is given. Let's check the other arrows:
• Domain 15: arrow to range 4? So \((15,4)\)?
• Domain 1: arrow to range 0? So \((1,0)\)?
• Domain 4: arrow to range 1? So \((4,1)\)?
• Domain 5: arrow to 6 (given as (5,6))? Wait, no, the given is (5,6), so that's correct. Then:
• For \((\square, 1)\): domain element 4 maps to 1, so 4.
• For \((\square, 4)\): domain element 15 maps to 4, so 15.
• For \((\square, 0)\): domain element 1 maps to 0, so 1.

Step2: Fill in the blanks

• First blank: \((4, 1)\) (since 4 in domain maps to 1 in range)
• Third blank: \((15, 4)\) (15 in domain maps to 4 in range)
• Fourth blank: \((1, 0)\) (1 in domain maps to 0 in range)

Wait, let's confirm:

• Ordered pair \((x, 1)\): x is 4 (since 4 → 1)
• Ordered pair \((15, 4)\): 15 → 4
• Ordered pair \((1, 0)\): 1 → 0

So:

• First blank: 4 (so \((4, 1)\))
• Third blank: 15 (so \((15, 4)\))
• Fourth blank: 1 (so \((1, 0)\))

Answer:

First blank: 4, Third blank: 15, Fourth blank: 1 (so the ordered pairs are \((4, 1)\), \((5, 6)\), \((15, 4)\), \((1, 0)\)) but for the blanks:

• \((\boldsymbol{4}, 1)\)
• \((5, 6)\) (given)
• \((\boldsymbol{15}, 4)\)
• \((\boldsymbol{1}, 0)\)

So the blanks are 4, 15, 1 (for the respective positions).