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 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.

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.
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Answer 1

To determine the graph of \(-f(x)\), we need to understand that this transformation reflects the original graph \(f(x)\) across the x-axis. This means that all the maximum points of the original graph become minimum points, and vice versa.

Here's how you can analyze the options given:

1. Identify key points on the original graph \(f(x)\) (like maximums and minimums).
2. Look for the option that corresponds to these transformations:
   • If \(f(x)\) has points at (x, y), then \(-f(x)\) will have points at (x, -y).
3. Check each option to see which one mirrors the y-values of \(f(x)\) across the x-axis.

If you can visually compare the options against the original graph and find which one reflects it accurately, you will be able to choose the correct one.

Without seeing the actual graphs, I cannot specify the correct answer, but the approach outlined above will guide you in choosing the correct option among 1, 2, 3, and 4.