Let's solve the problem step by step.

We are given a function $f(x) = -4x + 10$ and asked to find $g(x)$, the reflection of $f(x)$ across the $x$-axis. The reflection across the $x$-axis involves changing the sign of the entire function. In mathematical terms:

$g(x) = -f(x)$

Substitute $f(x) = -4x + 10$ into this formula:

$g(x) = -(-4x + 10)$

Simplify:

$g(x) = 4x - 10$

Thus, the reflected function is:

$g(x) = 4x - 10$

Final Answer:

$g(x) = 4x - 10$

Would you like me to explain this further or assist with any additional details?

Here are 5 related questions to deepen your understanding:

1. How would you reflect a function across the $y$-axis instead of the $x$-axis?
2. What happens to the slope and y-intercept of a function when reflected across the $x$-axis?
3. Can you generalize how to reflect a quadratic function across the $x$-axis?
4. How does reflecting a function affect its graph in terms of symmetry?
5. What transformations would you apply to reflect a function across both axes?

Tip: To reflect a function across the $x$-axis, simply negate the entire function!