Which set of ordered pairs represents a function? $$ \begin{array}{c}\{(0,7),(2,7),(4,7),(6,7),(8,7)\} \ \{(1,2),(2,3),(3,2),(2,1),(1,0)\} \ \{(5,1),(5,2),(5,3),(5,4),(5,5)\} \ \{(1,4),(2,4),(3,4),(4,3),(4,2)\}\end{array} $$

Question

UpStudy AI · Accepted Answer

To determine which set of ordered pairs represents a function, we need to ensure that **each input (x-value) is associated with exactly one output (y-value)**. In other words, no x-value should map to more than one y-value.

Let's analyze each set:

1. **$$\{(0,7),(2,7),(4,7),(6,7),(8,7)\}$$**
   - **x-values:** 0, 2, 4, 6, 8
   - **y-values:** All map to 7
   - **Analysis:** Each x-value maps to exactly one y-value (7). **This is a function.**

2. **$$\{(1,2),(2,3),(3,2),(2,1),(1,0)\}$$**
   - **x-values:** 1, 2, 3
   - **y-values:** 
     - x = 1 maps to 2 and 0
     - x = 2 maps to 3 and 1
   - **Analysis:** Both x = 1 and x = 2 map to multiple y-values. **This is not a function.**

3. **$$\{(5,1),(5,2),(5,3),(5,4),(5,5)\}$$**
   - **x-value:** 5
   - **y-values:** 1, 2, 3, 4, 5
   - **Analysis:** The single x-value (5) maps to multiple y-values. **This is not a function.**

4. **$$\{(1,4),(2,4),(3,4),(4,3),(4,2)\}$$**
   - **x-values:** 1, 2, 3, 4
   - **y-values:** 
     - x = 4 maps to 3 and 2
   - **Analysis:** x = 4 maps to multiple y-values. **This is not a function.**

**Conclusion:** Only the first set satisfies the definition of a function.

**Answer:** $$\{(0,7),(2,7),(4,7),(6,7),(8,7)\}$$
The first set $$\{(0,7),(2,7),(4,7),(6,7),(8,7)\}$$ represents a function.

Which set of ordered pairs represents a function? \( \begin{array}{c}\{(0,7),(2,7),(4,7),(6,7),(8,7)\} \\ \{(1,2),(2,3),(3,2),(2,1),(1,0)\} \\ \{(5,1),(5,2),(5,3),(5,4),(5,5)\} \\ \{(1,4),(2,4),(3,4),(4,3),(4,2)\}\end{array} \)

Solución de tutoría real

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Algebra Questions