Question

relation 2
relation 3
relation
domain
range
b
-9
m
6

Explanation:

Assuming the question is to determine if this relation is a function (a common problem in Algebra, a subfield of Mathematics), here's the solution:

Step1: Recall the definition of a function

A function is a relation where each element in the domain is paired with exactly one element in the range.

Step2: Check each domain element

• Domain element \( b \): Paired with \( 6 \) (from the line) and wait, no, looking at the diagram: Wait, let's re - examine. Wait, the domain elements are \( b \), \( h \), \( m \), \( t \).
• \( b \): Let's see the arrows. Wait, maybe I misread. Wait, \( h \) is paired to \( - 9 \), \( m \) is paired to \( - 9 \)? Wait, no, let's look again. Wait, the domain is \( b \), \( h \), \( m \), \( t \). The range is \( - 9 \), \( 6 \).
• \( b \): The arrow from \( b \) goes to \( 6 \)? Wait, no, maybe the diagram: Let's assume the arrows: \( b \) to \( 6 \)? Wait, no, the user's diagram: \( b \) has an arrow, \( h \) to \( - 9 \), \( m \) to \( - 9 \)? Wait, no, maybe I made a mistake. Wait, the key is: For a function, each domain element must have exactly one range element.
• Let's list the pairings:
• \( b \): Let's see the arrow from \( b \) – maybe to \( 6 \)? Wait, no, maybe the diagram is: \( b \) to \( 6 \), \( h \) to \( - 9 \), \( m \) to \( - 9 \), \( t \) to \( 6 \)? Wait, no, the original diagram: "b" has an arrow, "h" to "-9", "m" has an arrow, "t" to "6". Wait, maybe the correct way: Let's check if any domain element has more than one range element.
• If \( b \) is paired with two elements, or \( h \), \( m \), \( t \). Wait, maybe the diagram is such that \( h \) and \( m \) are both paired to \( - 9 \) (that's okay, multiple domain elements can map to the same range element, it's the reverse that's not allowed for functions: a domain element can't map to multiple range elements). Wait, maybe I misread. Wait, let's assume the question is "Is this relation a function?".
• Let's check each domain element:
• \( b \): How many arrows? If \( b \) has only one arrow (to one range element), \( h \) has one arrow (to \( - 9 \)), \( m \) has one arrow (to \( - 9 \) – that's fine, because two domain elements can map to the same range element), \( t \) has one arrow (to \( 6 \)). Wait, no, maybe the diagram is different. Wait, maybe the error is: If a domain element is paired with more than one range element, then it's not a function.
• Wait, maybe the diagram shows that \( b \) is paired with two elements? No, maybe I made a mistake. Wait, let's start over. The definition of a function: A relation is a function if and only if each input (domain element) has exactly one output (range element).
• So, let's list the domain elements: \( b \), \( h \), \( m \), \( t \).
• For \( b \): Let's see the arrow from \( b \) – suppose it goes to one element.
• For \( h \): arrow to \( - 9 \) (one element).
• For \( m \): arrow to, say, \( - 9 \) (one element).
• For \( t \): arrow to \( 6 \) (one element).
• Wait, but maybe \( b \) is paired with two elements? If not, then it's a function. Wait, maybe the diagram is such that \( b \) is paired with \( 6 \) and another element? No, maybe I misinterpret the diagram.
• Alternatively, maybe the question is to find the domain or range. Wait, the user didn't specify the question. Assuming the most common question: "Is this relation a function?".
• Let's check the vertical line test (for graphs, but for mappings, it's the domain - range pairing). A function has each domain element with exactly one range element.
• If in the diagram, each of \( b \), \( h \), \( m \), \( t \) is paired with exactly one range element (even if multiple do…

Answer:

If the question is "Is this relation a function?", the answer is Yes, because each element in the domain (\( b \), \( h \), \( m \), \( t \)) is paired with exactly one element in the range.