To find $f(x+1)$ for the function $f(x) = 3x - 7$, we need to substitute $x+1$ into the function in place of $x$.

Step-by-step Solution:

1. Substitute $x+1$ into the function: $f(x+1) = 3(x+1) - 7$

2. Expand the expression: $f(x+1) = 3x + 3 - 7$

3. Combine like terms: $f(x+1) = 3x - 4$

Conclusion:

$f(x+1) = 3x - 4$

Would you like more details or have any questions? Here are some related questions:

1. What is the value of $f(x+2)$ for the same function?
2. How do you find the inverse of the function $f(x) = 3x - 7$?
3. What is the value of $f(0)$ for the function $f(x) = 3x - 7$?
4. How does the slope of the function $f(x) = 3x - 7$ affect its graph?
5. What is the y-intercept of the function $f(x) = 3x - 7$?

Tip: When finding $f(a)$ for any given function $f(x)$, always substitute $a$ in place of $x$ and simplify.