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Given the graph of f(x)=(x−4)2+2

, which of the options is the graph of −f(x)
?


(1 point)
Responses

Option 1.
Option 1.

Option 2.
Option 2.

Option 3.
Option 3.

Option 4.

1 answer

To find the graph of \( -f(x) \) where \( f(x) = (x - 4)^2 + 2 \), we need to understand what happens when we negate the function.

  1. Original function: \( f(x) = (x - 4)^2 + 2 \)

    • This is a parabola that opens upwards, with its vertex at the point \( (4, 2) \).

  2. Negating the function: \( -f(x) = -((x - 4)^2 + 2) = -(x - 4)^2 - 2 \)

    • This transformation flips the graph of \( f(x) \) over the x-axis and also shifts it downward by 2 units.
    • The new vertex of \( -f(x) \) will be at \( (4, -2) \).

  3. In summary:

    • The vertex of \( -f(x) \) is at \( (4, -2) \).
    • The graph will open downwards.

To identify the correct graph among the options provided, look for a downward-opening parabola with its vertex at \( (4, -2) \).

If you can provide the visual representations of the options, I can help you identify which one matches the description.