https://file.aiquickdraw.com/mathbot/file/1729028153395wjl33i3v.jpg

To analyze the relation \(\{(-5,6), (4,6), (-5,4), (-6,-9)\}\), let’s go through the steps:

1. **Domain**: The domain of a relation is the set of all unique \( x \)-values.
   - From the relation \(\{(-5,6), (4,6), (-5,4), (-6,-9)\}\), the \( x \)-values are \(-5\), \(4\), and \(-6\).
   - Since \(-5\) appears twice, the domain is:
     \[
     \text{Domain} = \{-5, 4, -6\}
     \]

2. **Range**: The range of a relation is the set of all unique \( y \)-values.
   - The \( y \)-values here are \(6\), \(6\), \(4\), and \(-9\).
   - So, the range is:
     \[
     \text{Range} = \{6, 4, -9\}
     \]

3. **Function Test**: To determine if this relation is a function, check if each \( x \)-value is associated with only one \( y \)-value.
   - In this case, the \( x \)-value \(-5\) is associated with both \(6\) and \(4\).
   - Since an \( x \)-value is paired with more than one \( y \)-value, **this relation is not a function**.

### Summary
- **Domain**: \(\{-5, 4, -6\}\)
- **Range**: \(\{6, 4, -9\}\)
- **Function**: No, it is not a function because \(-5\) maps to both \(6\) and \(4\).

Would you like more details or have any questions?

---

Here are some related questions to expand on this topic:

1. What is the difference between a relation and a function?
2. How do you find the domain and range of a function or relation represented graphically?
3. What are one-to-one and onto functions, and how do they differ from basic functions?
4. How can you determine the domain and range of a function defined by an equation?
5. Why is it important to know if a relation is a function in real-world applications?

**Tip:** A relation is a function if and only if every \( x \)-value in the domain is mapped to a unique \( y \)-value.

Find the domain and the range of the relation. Determine whether the relation is a function. {(−5,6), (4,6), (−5,4), (−6,−9)}

Learn how to find the domain and range of the relation {(−5,6), (4,6), (−5,4), (−6,−9)} and determine whether it represents a function. This guide covers key concepts in functions and relations, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation