To find $f(n+9)$ for the function $f(x) = 5x + 1$:

1. Substitute $x = n + 9$ into the function: $f(n+9) = 5(n+9) + 1$

2. Distribute the 5: $f(n+9) = 5n + 45 + 1$

3. Simplify the expression: $f(n+9) = 5n + 46$

Therefore, $f(n+9) = 5n + 46$.

Would you like details or have any questions?

Here are some related questions to expand your understanding:

1. What is $f(3)$ for the function $f(x) = 5x + 1$?
2. How would you find the inverse of the function $f(x) = 5x + 1$?
3. What is the slope of the function $f(x) = 5x + 1$?
4. If $f(a) = 21$, what is the value of $a$ for the function $f(x) = 5x + 1$?
5. How would you graph the function $f(x) = 5x + 1$?
6. What is the y-intercept of the function $f(x) = 5x + 1$?
7. How does the function $f(x) = 5x + 1$ change if it is transformed to $f(x) = 5x + 4$?
8. How do you determine if the function $f(x) = 5x + 1$ is increasing or decreasing?

Tip: When working with linear functions, remember that the coefficient of $x$ (the slope) determines how steep the line is, and the constant term (the y-intercept) determines where the line crosses the y-axis.