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if the point (7,43) is on the graph of f(x) , what point must be on the graph of −f(−x)

Responses

(7,43)

(−7,−43)

(−7,43)

(7,−43)

1 answer

If the point (7, 43) is on the graph of \( f(x) \), it means that \( f(7) = 43 \).

We need to find the corresponding point on the graph of \( -f(-x) \).

  1. Substitute \( x = -7 \) into \( -f(-x) \): \[ -f(-(-7)) = -f(7) \]

  2. Now, since \( f(7) = 43 \): \[ -f(7) = -43 \]

Therefore, the point must be \( (-7, -43) \).

The correct response is: (−7,−43).