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: 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)

1 answer

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 \( f(x) = x^3 \).