Question

: When f(x) = x3
is reflected horizontally, the new function is f(x) =

Part B: Complete the table below for the horizontal reflection of the function f(x) =x3

x
−3
−2
−1
0 1 2 3
−f(x)

Answer 1

When the function \( f(x) = x^3 \) is reflected horizontally, it transforms according to the function \( f(x) = (-x)^3 \), which simplifies to:

\[ f(x) = -x^3 \]

This means the new function after a horizontal reflection is \( f(x) = -x^3 \).

### Part B: Complete the table for \( -f(x) \)
Now, we will evaluate \( -f(x) \) for the given values of \( x \):

1. For \( x = -3 \):
\[
-f(-3) = -(-3)^3 = -(-27) = 27
\]

2. For \( x = -2 \):
\[
-f(-2) = -(-2)^3 = -(-8) = 8
\]

3. For \( x = -1 \):
\[
-f(-1) = -(-1)^3 = -(-1) = 1
\]

4. For \( x = 0 \):
\[
-f(0) = -(0)^3 = -0 = 0
\]

5. For \( x = 1 \):
\[
-f(1) = -(1)^3 = -1
\]

6. For \( x = 2 \):
\[
-f(2) = -(2)^3 = -8
\]

7. For \( x = 3 \):
\[
-f(3) = -(3)^3 = -27
\]

### Completed Table:

| x | -f(x) |
|-----|-------|
| -3 | 27 |
| -2 | 8 |
| -1 | 1 |
| 0 | 0 |
| 1 | -1 |
| 2 | -8 |
| 3 | -27 |

This completes the table for the function \( -f(x) \) where \( f(x) = x^3 \).