Use the image to answer the question.

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 \(-f(x)\), we need to understand that the graph of \(-f(x)\) is the reflection of the graph of \(f(x)\) across the x-axis. This means that all the positive values of \(f(x)\) will become negative, and all the negative values will become positive.

If you have access to the original graph of \(f(x)\) and the different options, you would look for the option where:

• The peaks of \(f(x)\) (maximum points) are inverted to become valleys (minimum points) in \(-f(x)\).
• The troughs of \(f(x)\) (minimum points) are inverted to become peaks in \(-f(x)\).
• The x-intercepts remain the same, as they intersect the x-axis.

Once you identify which option reflects this transformation, that would be the correct answer.

Since I cannot see the actual graph or options, I recommend applying this reasoning to the images you have at hand.