Determine whether the relation is a function. Give the domain and the range of the relation.
​{(1​,2​),(1​,7​),(7​,2​),(7​,7​)}
Question content area bottom
Part 1
Is this a​ function?

A relation is a function if each input (or **domain element**) corresponds to exactly one output (or **range element**). In other words, no input can map to more than one output.

Given the relation \(\{(1, 2), (1, 7), (7, 2), (7, 7)\}\):

- The input \(1\) is paired with both \(2\) and \(7\).
- The input \(7\) is paired with both \(2\) and \(7\).

Since the input \(1\) maps to two different outputs (both \(2\) and \(7\)), and the input \(7\) also maps to two different outputs, **this relation is not a function**.

### Domain:
The domain is the set of all inputs. So, the domain is:
\[
\{1, 7\}
\]

### Range:
The range is the set of all outputs. So, the range is:
\[
\{2, 7\}
\]

### Conclusion:
- **Is this a function?** No.
- **Domain:** \(\{1, 7\}\)
- **Range:** \(\{2, 7\}\)

Would you like more details or have any questions?

Here are some related questions:
1. What conditions make a relation a function?
2. Can a function have repeated outputs for different inputs?
3. How would the relation change if we remove the pair \((1, 7)\)?
4. How do we graphically represent a function and a non-function?
5. What is the vertical line test for determining if a relation is a function?

**Tip:** In a function, every input must have exactly one output.

Determine whether the relation is a function. Give the domain and the range of the relation. {(1,2), (1,7), (7,2), (7,7)}

This problem explores whether a given relation {(1,2), (1,7), (7,2), (7,7)} is a function. Learn how to check for functions by analyzing the inputs and outputs, and identify the domain and range of the relation. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation