The question asks to find $g(x)$, the reflection of the given function $f(x) = x$ across the x-axis. Let's solve step by step:

Reflection across the x-axis:

When a function $f(x)$ is reflected across the x-axis, the reflection inverts the y-values. Mathematically, this means: $g(x) = -f(x).$

Given $f(x)$:

Since $f(x) = x$, substituting into $g(x) = -f(x)$, we get: $g(x) = -x.$

Final Answer:

$g(x) = -x$

Would you like a further breakdown of reflections or any related concepts?

5 Related Questions:

1. What happens if you reflect $f(x) = x$ across the y-axis instead?
2. How would the function change if reflected across the line $y = x$?
3. Can you describe a reflection for quadratic functions like $f(x) = x^2$?
4. What is the geometric interpretation of reflecting a function across the x-axis?
5. What happens when you reflect a function twice (e.g., across both axes)?

Tip:

Always remember that reflecting a function across the x-axis changes the sign of its output values ($y$-values), while reflecting across the y-axis changes the sign of its input values ($x$-values).