The expression \( \frac{3}{8} + x \) is a linear function. The range of a linear function depends on the domain of the variable \( x \).

1. **If no restrictions on \( x \)**: 
   If \( x \) is any real number (i.e., the domain is \( x \in \mathbb{R} \)), the range of \( \frac{3}{8} + x \) is also all real numbers. This is because as \( x \) increases or decreases, \( \frac{3}{8} + x \) can take any value from \( -\infty \) to \( \infty \).

   Hence, the range of \( \frac{3}{8} + x \) is:
   \[
   \text{Range} = \mathbb{R} = (-\infty, \infty)
   \]

2. **If there are domain restrictions**: 
   If you have specific limits on \( x \), the range would depend on those limits.

Would you like any clarification or details on this?

Here are 5 questions to explore related concepts:
1. What is the range of a quadratic function like \( x^2 + 2x + 1 \)?
2. How does the range change for \( f(x) = 1/(x+2) \)?
3. How can we determine the range of a logarithmic function?
4. How is the range of a piecewise function determined?
5. Can the range of a function be a set of discrete numbers?

**Tip:** For linear functions without restrictions, the range is always \( (-\infty, \infty) \).

Discover the range of the linear function 3/8 + x and learn how linear functions work. Understand that without restrictions, the range covers all real numbers, making this a great topic for students in Grades 6-8.

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