https://file.aiquickdraw.com/mathbot/file/1727046581960x6ah2dq4.jpg

The problem asks to transform the graph of \( y = g(x) \) to \( y = g(2x) \). To do this, you need to understand how the transformation \( y = g(2x) \) affects the graph.

### Transformation:
The equation \( y = g(2x) \) represents a **horizontal compression** by a factor of 2. This means that every x-coordinate of the original graph \( g(x) \) is halved, pulling the graph towards the y-axis.

#### Steps:
1. **Identify key points**: Choose some important points on the original graph, particularly the vertices and intercepts.
2. **Apply the transformation**: For each point \( (x, y) \) on the graph of \( g(x) \), the corresponding point on the graph of \( g(2x) \) will be \( \left( \frac{x}{2}, y \right) \).
3. **Sketch the new graph**: Once the points have been transformed, redraw the graph based on these points.

### Example with key points:
Suppose the original graph has the following points:
- \( (-4, 0) \)
- \( (-2, -4) \)
- \( (2, 4) \)

After applying the transformation \( x \to \frac{x}{2} \), the new points will be:
- \( (-2, 0) \)
- \( (-1, -4) \)
- \( (1, 4) \)

These points should then be used to plot the graph of \( y = g(2x) \).

Let me know if you would like a more detailed visual sketch or have any questions.

### 5 related questions:
1. What happens if we change the function to \( y = g( \frac{x}{2} ) \)?
2. How does the transformation \( y = g(-x) \) affect the graph?
3. What is the impact of applying \( y = 2g(x) \) to the graph?
4. Can you describe how a vertical shift affects the graph of a function?
5. How do you recognize symmetry in a graph?

**Tip**: Always track how the input variable \( x \) is affected by transformations such as stretching, compressing, reflecting, or shifting to correctly redraw graphs.

The graph of y = g(x) is shown. Draw the graph of y = g(2x).

Learn how to transform the graph of y = g(x) to y = g(2x), including a horizontal compression by a factor of 2. This problem covers key concepts in graph transformation and is suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation