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The given function is \(\frac{1}{22} f(x)\), and we are asked how this transformation changes the graph of \(y = f(x)\).

This involves a **vertical transformation**, as the factor \(\frac{1}{22}\) is multiplied directly to the output of the function \(f(x)\).

- If a function \(y = f(x)\) is multiplied by a constant \(c\), i.e., \(y = c f(x)\), the graph is affected **vertically**:
  - If \(0 < c < 1\), the graph is **compressed** vertically (it becomes shorter).
  - If \(c > 1\), the graph is **stretched** vertically (it becomes taller).

In this case, since \(\frac{1}{22}\) is a positive number less than 1, the graph of \(y = f(x)\) is **vertically compressed** by a factor of \(\frac{1}{22}\).

### Correct answer:
- **Vertically compressing the graph of \(f(x)\) by \(\frac{1}{22}\)**.

Would you like further details or explanations on this topic?

Here are 5 related questions to deepen your understanding:
1. How does multiplying the input of a function (i.e., \(f(2x)\)) affect its graph?
2. What happens to the graph if we multiply \(f(x)\) by a negative constant?
3. How does a horizontal stretch or compression differ from a vertical one?
4. How would adding a constant to \(f(x)\), like \(f(x) + 3\), shift the graph?
5. What transformation occurs if we replace \(x\) with \(-x\) in \(f(x)\)?

**Tip:** Always identify whether the transformation affects the input (horizontal) or output (vertical) when analyzing graph changes!

The graph of the function (1/22) f(x) can be obtained from the graph of y = f(x) by one of the following actions: horizontally stretching or compressing or vertically stretching or compressing by 22 or 1/22?

Learn how the graph of the function (1/22) f(x) is obtained by vertically compressing the graph of y = f(x) by a factor of 1/22. This transformation affects the vertical scaling of the function. Suitable for students in Grades 9-11 studying function transformations.

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