Question

the table shows the points of a function. complete the table to show the points after a reflection about x-axis

x = -4, -3,-2,-1,0
f(x)=8,2,0,2,8

now, complete the table to show that h(x) is the reflection about the x-axis of the function

Answer 1

To reflect the points of a function \( f(x) \) about the x-axis, you change the sign of the \( y \)-values (the function values). This means that if \( f(x) = y \), then the reflection \( h(x) \) will be \( h(x) = -y \).

Here are the points from your original table, along with their reflections:

| \( x \) | \( f(x) \) | \( h(x) \) |
|----------|-------------|--------------|
| -4 | 8 | -8 |
| -3 | 2 | -2 |
| -2 | 0 | 0 |
| -1 | 2 | -2 |
| 0 | 8 | -8 |

So, the complete table showing the reflection about the x-axis is:

| \( x \) | \( f(x) \) | \( h(x) \) |
|----------|-------------|--------------|
| -4 | 8 | -8 |
| -3 | 2 | -2 |
| -2 | 0 | 0 |
| -1 | 2 | -2 |
| 0 | 8 | -8 |