To determine whether each set of ordered pairs represents a function, we need to check if each input (or [tex]\( x \)[/tex]-value) is associated with exactly one output (or [tex]\( y \)[/tex]-value). In simple terms, no [tex]\( x \)[/tex]-value should be repeated with different [tex]\( y \)[/tex]-values.
Let's analyze each set of ordered pairs in detail:
1. [tex]\((2,3), (6,-5), (-1,3)\)[/tex]:
- [tex]\( x \)[/tex]-values: [tex]\( 2, 6, -1 \)[/tex]
- All [tex]\( x \)[/tex]-values are unique.
Therefore, this set represents a function.
2. [tex]\((1,9), (-3,-2), (1,-4)\)[/tex]:
- [tex]\( x \)[/tex]-values: [tex]\( 1, -3, 1 \)[/tex]
- The [tex]\( x \)[/tex]-value [tex]\( 1 \)[/tex] is repeated with different [tex]\( y \)[/tex]-values ([tex]\( 9 \)[/tex] and [tex]\( -4 \)[/tex]).
Therefore, this set does not represent a function.
3. [tex]\((7,-4), (0,9), (2,-2)\)[/tex]:
- [tex]\( x \)[/tex]-values: [tex]\( 7, 0, 2 \)[/tex]
- All [tex]\( x \)[/tex]-values are unique.
Therefore, this set represents a function.
4. [tex]\((0,3), (0,7), (4,0)\)[/tex]:
- [tex]\( x \)[/tex]-values: [tex]\( 0, 0, 4 \)[/tex]
- The [tex]\( x \)[/tex]-value [tex]\( 0 \)[/tex] is repeated with different [tex]\( y \)[/tex]-values ([tex]\( 3 \)[/tex] and [tex]\( 7 \)[/tex]).
Therefore, this set does not represent a function.
5. [tex]\((-6,5), (-5,6), (8,2)\)[/tex]:
- [tex]\( x \)[/tex]-values: [tex]\( -6, -5, 8 \)[/tex]
- All [tex]\( x \)[/tex]-values are unique.
Therefore, this set represents a function.
In summary:
1. [tex]\((2,3), (6,-5), (-1,3)\)[/tex] - Function
2. [tex]\((1,9), (-3,-2), (1,-4)\)[/tex] - Not a Function
3. [tex]\((7,-4), (0,9), (2,-2)\)[/tex] - Function
4. [tex]\((0,3), (0,7), (4,0)\)[/tex] - Not a Function
5. [tex]\((-6,5), (-5,6), (8,2)\)[/tex] - Function
So the final results are:
- [tex]\((2,3), (6,-5), (-1,3)\)[/tex] - Function
- [tex]\((1,9), (-3,-2), (1,-4)\)[/tex] - Not a Function
- [tex]\((7,-4), (0,9), (2,-2)\)[/tex] - Function
- [tex]\((0,3), (0,7), (4,0)\)[/tex] - Not a Function
- [tex]\((-6,5), (-5,6), (8,2)\)[/tex] - Function
