https://file.aiquickdraw.com/mathbot/file/1727454852461wzwsu5d3.jpg

The question in the image asks about translating the function \( f(x) \) by 2 units up and vertically shrinking it with a scale factor of 0.5. 

Let's break down the transformations:
1. **Vertical shrinking by 0.5** means multiplying the function by 0.5. This gives: 
   \[ g(x) = 0.5 \cdot f(x) \]
2. **Translating 2 units up** means adding 2 to the function. So we add 2 to the result from step 1:
   \[ g(x) = 0.5 \cdot f(x) + 2 \]

Thus, the correct rule describing this transformation is:

\[
g(x) = 0.5f(x) + 2
\]

From the given options, the correct one is the **blue box**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How does horizontal scaling affect the graph of a function?
2. What is the difference between translating a function up and shifting it horizontally?
3. How do you reflect a function over the x-axis or y-axis?
4. Can a function be transformed by both horizontal and vertical stretching simultaneously?
5. How would you translate a function 3 units to the right?

**Tip:** Vertical transformations affect the output (y-values) of a function, while horizontal transformations affect the input (x-values).

The function f(x) was translated 2 units up and vertically shrunk with a scale factor of 0.5. Which rule describes this transformation?

Learn how to vertically shrink a function with a scale factor of 0.5 and translate it 2 units up. This problem covers key concepts in function transformations, including vertical scaling and translations. Suitable for students in Grades 8-10.

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