https://file.aiquickdraw.com/mathbot/file/1726985305816mpa4qhp9.jpg

In the image provided, you are asked to identify the transformation from \( f(x) \) to \( g(x) \) based on the graph.

- \( f(x) \) is the solid line.
- \( g(x) \) is the dotted line.

### Observations:
1. The graph of \( g(x) \) appears to be a vertical shift of the graph of \( f(x) \) downwards. The two graphs have the same shape, but \( g(x) \) is lower on the y-axis compared to \( f(x) \), indicating a vertical translation.

### Answer:
The correct description of the transformation from \( f(x) \) to \( g(x) \) is **b. Vertical shift**.

Would you like a more detailed explanation, or do you have any other questions?

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Here are 5 related questions to deepen understanding:
1. What happens to the function when it undergoes a horizontal shift versus a vertical shift?
2. How would the equation of \( f(x) \) change if it were vertically shifted by 3 units downwards?
3. What is the effect of a vertical stretch on the graph of a function?
4. How can you identify a horizontal shift just by looking at the equation of a function?
5. How would a vertical stretch or compression affect the y-values of a function?

### Tip:
When identifying transformations, observe the changes in key points on the graph, such as the intercepts and relative maxima/minima, to quickly recognize shifts and stretches.

Which description matches the transformation from f(x) to g(x) shown?

In this problem, you will identify a transformation from f(x) to g(x) based on a graphical representation. The problem focuses on determining if the transformation is a vertical or horizontal shift, with detailed visual cues. Suitable for students in Grades 10-12.

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