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).