Question

Create a table of values that models the function in the graph reflected over the x-axis.

Answer 1

To create a table of values for a function reflected over the x-axis, you'll need to start with a given function. For the sake of this example, let’s assume we have a function \( f(x) \) and we want to find the reflection of this function, which we can denote as \( -f(x) \).

Here’s an example using a simple function, say \( f(x) = x^2 \):

### Original Function: \( f(x) = x^2 \)

Let's define the function over the range of \( x \) values from -3 to 3 and calculate \( f(x) \) along with its reflection.

| \( x \) | \( f(x) = x^2 \) | Reflected \( -f(x) \) |
|---------|------------------|-----------------------|
| -3 | 9 | -9 |
| -2 | 4 | -4 |
| -1 | 1 | -1 |
| 0 | 0 | 0 |
| 1 | 1 | -1 |
| 2 | 4 | -4 |
| 3 | 9 | -9 |

### Explanation:
- The **first column** represents the \( x \) values.
- The **second column** shows the original function \( f(x) = x^2 \).
- The **third column** depicts the reflection over the x-axis, represented by \( -f(x) \).

You can replace \( f(x) = x^2 \) with any other function to generate your own table of values for that specific function and its reflection over the x-axis. Just remember, the reflected value will always be the negative of the original function value at each corresponding \( x \).