Question

(1 point)
Part A: 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

To find the horizontal reflection of the function \( f(x) = x^3 \), we need to replace \( x \) with \( -x \).

### Part A:
The new function after the horizontal reflection is:
\[
f(x) = (-x)^3 = -x^3
\]

### Part B:
We need to complete the table for the function \( -f(x) = -x^3 \). First, let's calculate \( -f(x) \) for the given values of \( x \):

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

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

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

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

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

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

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

Now let's complete the table.

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

So the completed table for \( -f(x) \) is:

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