Complete the table to show that h(x)

Question

is the reflection about the origin of the function f(x)

x f(x)
0 0
1 1
2 8
x h(x)
0 0
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Answer 1

To show that $h(x)$ is the reflection about the origin of the function $f(x)$, we need to find $h(x)$ such that $h(x)=-f(-x)$.

Let's fill in the table for $h(x)$ based on the values of $f(x)$:

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

Explanation:

• For $x=0$:

  • $f(0)=0$
  • $h(0)=-f(-0)=-f(0)=-0=0$

• For $x=1$:

  • $f(1)=1$
  • $h(1)=-f(-1)$ (need to find $f(-1)$; if it’s not provided, we cannot calculate).

However, based on the reflection about the origin concept, it's typically $-f(1)$:

• $h(1)=-f(1)=-1$

• For $x=2$:

  • $f(2)=8$
  • $h(2)=-f(-2)$ (again, need $f(-2)$ value).

Just for reflection:

• $h(2)=-f(2)=-8$

We provided values for $h(x)$ based on the pattern of reflection across the origin, which demonstrates that $h(x)$ reflects $f(x)$ appropriately. If you have specific values for $f(-1)$ and $f(-2)$, please provide, and we can adjust accordingly.