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

The graph of −f(x)
is option 3.

Answer 1

To determine which option represents the graph of \(-f(x)\), we need to understand that graphing \(-f(x)\) reflects the original graph \(f(x)\) across the x-axis. This means that all the y-values of the wave will be inverted.

If the wave has peaks above the x-axis, the corresponding peaks in \(-f(x)\) will be the same distance below the x-axis, and therefore the troughs will become peaks and vice versa.

To identify the correct option based on the reflection:

1. Look at the original graph \(f(x)\) and find where the peaks and troughs occur.
2. For each peak above the x-axis, check if the corresponding point in the options is below the x-axis at the same distance.
3. Likewise, for each trough below the x-axis, check if the corresponding point in the options is above the x-axis at the same height.

Since I cannot see the graphs, I recommend you to evaluate each option in this way. Whichever option has the inverted peaks and troughs compared to the original graph \(f(x)\) will be the graph of \(-f(x)\). Choose that option as your answer.