Complete the table to show that h(x)

To reflect the function \( f(x) \) about the origin, we use the transformation \( h(x) = -f(x) \). This means that for each \( x \) value, \( h(x) \) will be the negative of the corresponding \( f(x) \).

Given the table for \( f(x) \):

| \( x \) | \( f(x) \) | |---------|------------| | 0 | 0 | | 1 | 1 | | 2 | 8 |

We can now calculate \( h(x) \) for the same \( x \) values:

1. For \( x = 0 \): \( h(0) = -f(0) = -0 = 0 \)
2. For \( x = 1 \): \( h(1) = -f(1) = -1 \)
3. For \( x = 2 \): \( h(2) = -f(2) = -8 \)

Now we can fill in the second table for \( h(x) \):

| \( x \) | \( h(x) \) | |---------|------------| | 0 | 0 | | 1 | -1 | | 2 | -8 |

Here is the completed table for \( h(x) \):

| \( x \) | \( h(x) \) | |---------|------------| | 0 | 0 | | 1 | -1 | | 2 | -8 |