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The task asks you to draw the graph of \( y = g(-x) \), based on the graph of \( y = g(x) \), which is provided.

To graph \( y = g(-x) \), you need to reflect the given graph \( y = g(x) \) across the **y-axis**. This is because the transformation \( g(-x) \) reflects any point on the graph over the y-axis. Here's how to interpret the reflection:

1. For each point \( (x, y) \) on the graph of \( y = g(x) \), the corresponding point on the graph of \( y = g(-x) \) will be \( (-x, y) \).
   
2. The entire line shown in your original graph (which is decreasing from left to right) will be flipped horizontally, so it will now decrease from right to left after the reflection.

If you follow these steps, you will end up with a graph that mirrors the original one across the y-axis.

Do you want to go over how to reflect specific points or need further details? Let me know!

Here are 5 related questions to deepen your understanding:
1. How would you describe the transformation \( y = g(-x) \) in terms of symmetry?
2. What would happen if the transformation was \( y = -g(x) \) instead?
3. How does reflecting a graph over the x-axis differ from reflecting over the y-axis?
4. Can you predict how the graph would look if both \( x \) and \( y \) were reflected, i.e., \( y = -g(-x) \)?
5. What is the significance of knowing these transformations in practical applications, like physics or engineering?

**Tip:** Reflecting across the y-axis (as in \( y = g(-x) \)) changes the direction of the graph horizontally but leaves the vertical shape unchanged.

The graph of y = g(x) is shown. Draw the graph of y = g(-x).

Learn how to reflect the graph of y = g(x) across the y-axis to obtain y = g(-x). This guide covers graph transformations, specifically focusing on coordinate geometry and symmetry. Suitable for students in Grades 9-11.

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