Question

Question
Use the image to answer the question.

Five labeled sinusoidal waves are plotted on a coordinate plane.

Describe the transformation of the graph of f(x)
to the graph labeled Option 3.

(1 point)
Responses

Option 3 is the graph of −f(x)
.
Option 3 is the graph of f left parenthesis negative x right parenthesis .

Option 3 is the graph of f(−x)
.
Option 3 is the graph of f left parenthesis negative x right parenthesis .

Option 3 is the graph of f(x)+1
.
Option 3 is the graph of f left parenthesis negative x right parenthesis .

Option 3 is the graph of −f(−x)
.
Option 3 is the graph of f left parenthesis negative x right parenthesis .
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Answer 1

To determine how the graph of \( f(x) \) transforms to match the graph labeled as Option 3, we need to analyze the transformations of sinusoidal functions.

### Key Transformations:
1. **Reflection**:
- \( -f(x) \): Reflects across the x-axis.
- \( f(-x) \): Reflects across the y-axis.

2. **Vertical Shift**:
- \( f(x) + k \): Shifts the graph up by \( k \).

3. **Horizontal Shift**:
- \( f(x - h) \): Shifts the graph to the right by \( h \).

### Analyzing Options:
Since you have multiple options related to transformations of \( f(x) \), we’ll see which can describe Option 3 correctly:

- **Option 1: \( -f(x) \)**
This describes a reflection over the x-axis.

- **Option 2: \( f(-x) \)**
This describes a reflection over the y-axis.

- **Option 3: \( -f(-x) \)**
This is a reflection over both axes (first across the y-axis and then the x-axis).

### Conclusion:
Without the actual visual representation, if Option 3 appears to be a reflection of the original graph across both axes, then the correct response would be:

**Option 3 is the graph of \( -f(-x) \).**

If that's not the case, and you know what the transformation looks like, please share that info for a more accurate response!