https://file.aiquickdraw.com/mathbot/file/1725378018403mg2ew0dk.jpg

The image shows a problem asking to identify the correct graph for a set of transformations applied to a parent function. The transformations are:

- Reflect in the \(x\)-axis
- Stretch vertically by a factor of \(3\)
- Translate \(4\) units to the left
- Translate \(2\) units down
- Rotate \(90^\circ\) clockwise

Given these transformations, let's analyze them step by step:

1. **Reflection in the \(x\)-axis**: This inverts the graph over the \(x\)-axis.
2. **Vertical Stretch by a factor of \(3\)**: This makes the graph three times taller.
3. **Translation 4 units left**: This shifts the graph 4 units to the left.
4. **Translation 2 units down**: This shifts the graph 2 units down.
5. **Rotation \(90^\circ\) clockwise**: This rotates the graph \(90^\circ\) in the clockwise direction.

Given these transformations, the correct graph should reflect these changes. By examining the options provided, the one that corresponds to all these transformations will be the correct one.

Based on the image, **Option C** is the graph that reflects the transformations correctly.

Would you like further details on any of these transformations, or do you have any other questions?

Here are 5 related questions to expand your understanding:

1. What happens to a graph when it is reflected over the \(y\)-axis instead of the \(x\)-axis?
2. How would the graph change if it were translated up instead of down?
3. What effect does a horizontal stretch have on the shape of a graph?
4. How do rotations by \(90^\circ\) differ between clockwise and counterclockwise directions?
5. Can you describe the sequence of transformations that would reverse the effects described here?

**Tip**: When performing multiple transformations, the order in which you apply them can sometimes affect the final graph, especially when rotations are involved.

Sketch a graph given the following features: 
- Reflect in the x-axis 
- Stretch vertically by a factor of 3 
- Translate 4 units to the left 
- Translate 2 units down 
- Rotate 90° clockwise 
Choose the graph that best matches these transformations from the options provided.

Learn how to identify and apply transformations to a graph, including reflection over the x-axis, vertical stretching, horizontal and vertical translations, and 90° clockwise rotation. Suitable for students in Grades 9-12, this example illustrates step-by-step how each transformation affects the graph.

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