https://file.aiquickdraw.com/mathbot/file/1726080496766yfah4ing.jpg

The question asks for the equation of \( g(x) \), which is a reflection of the function \( f(x) = 3x - 4 \) across the x-axis.

### Key Concept: Reflection across the x-axis
- When reflecting a function across the x-axis, you negate the output of the function (i.e., change the sign of the y-values).
- For any function \( f(x) \), the reflected function across the x-axis is \( g(x) = -f(x) \).

### Solution:
1. The given function is \( f(x) = 3x - 4 \).
2. The reflection across the x-axis gives us:
   \[
   g(x) = -[3x - 4] = -3x + 4
   \]
   
Thus, the equation of \( g(x) \) is \( g(x) = -3x + 4 \).

### Answer:
The correct option is:  
\[
g(x) = -3x + 4
\]

Would you like further details or have any questions?

Here are five related questions you might find helpful:
1. How do you reflect a function across the y-axis instead of the x-axis?
2. What happens to the graph of a function if it's reflected across both axes?
3. Can you explain how to reflect a quadratic function across the x-axis?
4. How does reflecting a function across the x-axis affect its domain and range?
5. How would the graph of \( f(x) = 3x - 4 \) change if reflected across the y-axis?

**Tip:** When reflecting functions, always focus on the output of the function; the sign change directly affects the y-values (for x-axis reflection) or the x-values (for y-axis reflection).

Graph f(x) = 3x - 4 and the function g, a reflection of the graph of f across the x-axis. What is the equation of g(x)?

Find the reflection of the function f(x) = 3x - 4 across the x-axis. This problem involves key algebraic concepts and the reflection theorem. Suitable for students in Grades 9-11.

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