Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

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
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.