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Determine if each set of ordered pairs represents a function.

A. [tex]\((2, 3), (6, -5), (-1, 3)\)[/tex]

B. [tex]\((1, 9), (-3, -2), (1, -4)\)[/tex]

C. [tex]\((7, -4), (0, 9), (2, -2)\)[/tex]

D. [tex]\((0, 3), (0, 7), (4, 0)\)[/tex]

E. [tex]\((-6, 5), (-5, 6), (8, 2)\)[/tex]

Options:
1. Function
2. Not a Function

Sagot :

GinnyAnswer
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
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