Answer :
To determine which ordered pair, if any, needs to be removed for the mapping to represent a function, we must verify the definition of a function. In mathematics, a function is defined as a relationship where each input [tex]\( x \)[/tex] has a unique output [tex]\( y \)[/tex].
1. Let's list the given ordered pairs:
[tex]\[ (-3, -4), (-2, -1), (1, -3), (3, 7) \][/tex]
2. Extract and list the [tex]\( x \)[/tex]-values from these pairs:
[tex]\[ -3, -2, 1, 3 \][/tex]
3. Determine if any [tex]\( x \)[/tex]-values are repeated:
- [tex]\( -3 \)[/tex] appears once.
- [tex]\( -2 \)[/tex] appears once.
- [tex]\( 1 \)[/tex] appears once.
- [tex]\( 3 \)[/tex] appears once.
Since all [tex]\( x \)[/tex]-values are unique, each input is associated with exactly one output. Therefore, no repeated [tex]\( x \)[/tex]-values exist among the ordered pairs. This confirms that the relationship as given already satisfies the definition of a function.
Thus, there is no need to remove any ordered pair. The mapping already represents a function.
So, the conclusion is:
[tex]\[ \boxed{\text{None}} \][/tex]
1. Let's list the given ordered pairs:
[tex]\[ (-3, -4), (-2, -1), (1, -3), (3, 7) \][/tex]
2. Extract and list the [tex]\( x \)[/tex]-values from these pairs:
[tex]\[ -3, -2, 1, 3 \][/tex]
3. Determine if any [tex]\( x \)[/tex]-values are repeated:
- [tex]\( -3 \)[/tex] appears once.
- [tex]\( -2 \)[/tex] appears once.
- [tex]\( 1 \)[/tex] appears once.
- [tex]\( 3 \)[/tex] appears once.
Since all [tex]\( x \)[/tex]-values are unique, each input is associated with exactly one output. Therefore, no repeated [tex]\( x \)[/tex]-values exist among the ordered pairs. This confirms that the relationship as given already satisfies the definition of a function.
Thus, there is no need to remove any ordered pair. The mapping already represents a function.
So, the conclusion is:
[tex]\[ \boxed{\text{None}} \][/tex]
