Question

Question
Use the image to answer the question.

Five labeled sinusoidal waves are plotted on a coordinate plane.

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

(1 point)
Responses

The graph of −f(x)
is option 1.
The graph of negative f left parenthesis x right parenthesis is option 1.

The graph of −f(x)
is option 3.
The graph of negative f left parenthesis x right parenthesis is option 3.

The graph of −f(x)
is option 4.
The graph of negative f left parenthesis x right parenthesis is option 4.

The graph of −f(x)
is option 2.
The graph of negative f left parenthesis x right parenthesis is option 2.
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Answer 1

To determine which option represents the graph of \(-f(x)\), you need to understand that the transformation from \(f(x)\) to \(-f(x)\) reflects the graph of \(f(x)\) across the x-axis.

If you have access to the sinusoidal wave graph for \(f(x)\):

1. Identify how the original graph \(f(x)\) behaves.
2. For \(-f(x)\), every point on \(f(x)\) will reflect to an equal distance below the x-axis.

For example:
- If \(f(x)\) has a peak at \(y = a\), then the corresponding value on \(-f(x)\) will be at \(y = -a\).
- Similarly, if \(f(x)\) has a trough at \(y = -b\), then \(-f(x)\) will have a peak at \(y = b\).

Once you apply this reflection concept to each of the options, you should be able to identify which option correctly represents the transformation to \(-f(x)\).

If you can’t see the actual graphs, I suggest comparing them based on the properties outlined above. Look for the graph that has peaks where there were troughs and vice versa.

If you require specific assistance after viewing the graphs, please describe the key features of each option, and I can help you identify the correct graph.