To solve the difference quotient for the given function $f(x) = 3x + 4$, we need to compute:

$\frac{f(x+h) - f(x)}{h}$

Step-by-step solution:

1. Find $f(x + h)$: Substitute $x + h$ into the function $f(x) = 3x + 4$: $f(x + h) = 3(x + h) + 4 = 3x + 3h + 4$

2. Compute the difference $f(x + h) - f(x)$: Now subtract $f(x)$ from $f(x + h)$: $f(x + h) - f(x) = (3x + 3h + 4) - (3x + 4) = 3x + 3h + 4 - 3x - 4 = 3h$

3. Simplify the difference quotient: Now divide by $h$: $\frac{f(x+h) - f(x)}{h} = \frac{3h}{h} = 3$

Thus, the simplified difference quotient is:

$\frac{f(x+h) - f(x)}{h} = 3$

Would you like further clarification or more details on this process?

Here are 5 related questions to consider:

1. How does the difference quotient relate to the concept of a derivative?
2. Can we apply the difference quotient to non-linear functions, and how would the process differ?
3. What is the geometric interpretation of the difference quotient for a linear function like $f(x) = 3x + 4$?
4. How does the constant term (like the $+4$ in this function) affect the difference quotient?
5. How can we use the difference quotient to approximate instantaneous rates of change?

Tip: The difference quotient is essentially the average rate of change over an interval, and it's a key step in finding the derivative of a function.