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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?

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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!

Find g(x), where g(x) is the reflection across the x-axis of f(x) = -4x + 10. Write your answer in the form mx + b, where m and b are integers.

Learn how to find g(x), the reflection of f(x) = -4x + 10 across the x-axis. This step-by-step solution explains how to apply transformation rules to determine the reflected function in the form mx + b. Suitable for students in Grades 8-10.

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