you reflect the following line over the x axis f(x)=x

When you reflect the line \( f(x) = x \) over the x-axis, the transformation changes the sign of all the \( y \)-coordinates of the points on the line. 

The reflection over the x-axis can be represented by multiplying the function by \(-1\):

\[
g(x) = -f(x) = -x
\]

So, the reflected function is:

\[
g(x) = -x
\]

This means that every point \( (x, y) \) on the original line \( f(x) = x \) will be transformed to \( (x, -y) \) on the reflected line \( g(x) = -x \).

### Summary:
The reflection of the line \( f(x) = x \) over the x-axis results in the line \( g(x) = -x \).

Would you like more details or have any questions?

Here are five related questions:

1. What would be the result of reflecting \( f(x) = x \) over the y-axis?
2. How would the graph of \( f(x) = x \) change if reflected over the line \( y = x \)?
3. What is the general formula for reflecting a function over the x-axis?
4. How does the reflection of a quadratic function, such as \( f(x) = x^2 \), differ from that of a linear function?
5. If \( f(x) = 2x \), what is the reflection of this line over the x-axis?

**Tip:** Reflection over the x-axis changes the sign of the \( y \)-coordinates of all points on the graph, effectively flipping the graph upside down.

Learn about reflecting the line f(x) = x over the x-axis in coordinate geometry. Understand how this transformation changes the graph by flipping it upside down and reversing the y-coordinates. Suitable for students studying transformations and coordinate geometry in Grades 9-12.

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