The function you have given is:

\[
f(x) = \frac{1}{x + 3}
\]

### Key Points:
1. **Domain**: The function is undefined when \(x = -3\), because division by zero is not allowed. Thus, the domain of the function is all real numbers except \(x = -3\).
   \[
   \text{Domain}: (-\infty, -3) \cup (-3, \infty)
   \]

2. **Asymptotes**: The function has:
   - A **vertical asymptote** at \(x = -3\), because the denominator approaches zero as \(x\) approaches \(-3\).
   - A **horizontal asymptote** at \(y = 0\), because as \(x\) goes to infinity, the value of the function approaches 0.

3. **Graph Behavior**: 
   - For \(x > -3\), the function is positive and decreasing.
   - For \(x < -3\), the function is negative and increasing.

Would you like more details on any specific aspect of this function?

### 5 Related Questions:
1. What are the intercepts of this function?
2. How do you find the vertical and horizontal asymptotes of a function?
3. Can this function be differentiated and integrated?
4. How does the graph of this function look like?
5. What happens to the function as \(x\) approaches infinity?

**Tip**: Always check for any restrictions on the domain of a function when dealing with fractions.

Explore the rational function f(x) = 1 / (x + 3), including its domain, vertical and horizontal asymptotes, and graph behavior. This solution covers key concepts in rational functions, suitable for students in Grades 10-12.

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