What is the range of the constant function 1 ?

Answer

To find the range of the constant function \( f(x) = 1 \), we can follow these steps:

### Step-by-Step Solution:

1. **Definition of a Constant Function**: A constant function is defined as a function that always returns the same value regardless of the input. In this case, the function is \( f(x) = 1 \).

2. **Understanding the Domain**: The domain of a function is the set of all possible input values (x-values). For a constant function, the domain can be any set of real numbers, such as all real numbers \( \mathbb{R} \), natural numbers \( \mathbb{N} \), etc.

3. **Evaluating the Function**: For any value of \( x \) in the domain, the output of the function \( f(x) \) will always be 1. This means:
- If \( x_1 \) is any value in the domain, then \( f(x_1) = 1 \).
- If \( x_2 \) is any other value in the domain, then \( f(x_2) = 1 \).

4. **Determining the Range**: The range of a function is the set of all possible output values (y-values). Since the output of the function \( f(x) = 1 \) is always 1, the range will only include this single value.

5. **Conclusion**: Therefore, the range of the constant function \( f(x) = 1 \) is \( \{ 1 \} \).

### Final Answer:
The range of the constant function \( f(x) = 1 \) is \( \{ 1 \} \).