Here is the graph of the function $f(x) = \frac{x+1}{x+3}$. The red dashed line shows the vertical asymptote at $x = -3$, where the function is undefined, and the blue dashed line shows the horizontal asymptote at $y = 1$.

Would you like more details or have any questions?

Here are some related questions:

1. How do you determine the horizontal asymptote of a rational function?
2. What are the intercepts of the function $f(x) = \frac{x+1}{x+3}$?
3. How does the function behave as $x$ approaches the vertical asymptote?
4. What is the significance of the horizontal asymptote at $y = 1$?
5. How do you find the domain of $f(x) = \frac{x+1}{x+3}$?

Tip: When graphing rational functions, it's essential to consider both vertical and horizontal asymptotes to understand the function's long-term behavior.