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.

Learn how to calculate f(n+9) for the linear function f(x) = 5x + 1 using step-by-step solutions. This problem involves function notation and the distributive property. Suitable for students in Grades 7-9.

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