Determine whether the relation is a function. Give the domain and the range of the relation. $$ \{(3,1),(3,8),(6,1),(6,8)\} $$ Is this a function? Yes No

Question

UpStudy AI · Accepted Answer

To determine whether the given relation is a function, we need to check if each input (or first element of the ordered pairs) corresponds to exactly one output (or second element of the ordered pairs).

The given relation is:
$$
\{(3,1),(3,8),(6,1),(6,8)\}
$$

### Step 1: Check for uniqueness of outputs
- The first element $$3$$ corresponds to two different outputs: $$1$$ and $$8$$.
- The first element $$6$$ also corresponds to two different outputs: $$1$$ and $$8$$.

Since the same input $$3$$ has two different outputs, and the same input $$6$$ also has two different outputs, this relation does not satisfy the definition of a function.

### Conclusion
- **Is this a function?** No

### Step 2: Determine the domain and range
- **Domain**: The set of all first elements (inputs) in the ordered pairs.
  - From the relation, the first elements are $$3$$ and $$6$$.
  - Therefore, the domain is $$\{3, 6\}$$.

- **Range**: The set of all second elements (outputs) in the ordered pairs.
  - From the relation, the second elements are $$1$$ and $$8$$.
  - Therefore, the range is $$\{1, 8\}$$.

### Final Answer
- **Is this a function?** No
- **Domain**: $$\{3, 6\}$$
- **Range**: $$\{1, 8\}$$
This relation is not a function. The domain is $$\{3, 6\}$$ and the range is $$\{1, 8\}$$.

Determine whether the relation is a function. Give the domain and the range of the relation. \( \{(3,1),(3,8),(6,1),(6,8)\} \) Is this a function? Yes No

Real Tutor Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Pre Algebra Questions