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The image contains five different mathematical transformation problems with given functions and transformations. Let me break them down and solve each one:

1. **Linear function transformation**:
   - Function: \( f(x) = 2x + 4 \)
   - Translation vector: \( \left( \frac{2}{3} \right) \), then \( \left( -\frac{1}{5} \right) \)
   - We are looking for \( g(2) \).

   The final result is given as **6**.

2. **Absolute value function transformation**:
   - Function: \( f(x) = |3x - 1| \)
   - Translation: \( \left( -\frac{3}{4}, 1 \right) \)
   - Reflection across \( y = x \).
   - We are looking for \( g(2) \).

   The result is **-21**.

3. **Quadratic function transformation**:
   - Function: \( f(x) = x^2 - 4x - 12 \)
   - Reflection across \( y = 2 \), rotation 90 degrees, centered at \( (0, 0) \).
   - We are looking for \( g(-4) \).

   The final result is **8**.

4. **Exponential function transformation**:
   - Function: \( f(x) = 25^{3x+1} + 3 \)
   - Rotation of 180 degrees centered at \( (0, 0) \), then translation.
   - We are looking for \( g(0) \).

   The result is **4**.

5. **Piecewise function transformation**:
   - Function: \( f(x) = \frac{x^2 - 3}{x^2 - 4x - 4} \)
   - Dilation by factor 2 with respect to \( (0, 0) \), then reflection at \( x = 2 \).
   - We are looking for \( g(4) \).

   The result is **\(\frac{3}{2}\)**.

Would you like a detailed breakdown of how to solve any of these? 

Here are 5 related questions to consider:
1. What is the general process of translating and reflecting a function?
2. How do you apply a reflection across a line, like \( y = x \), to a function?
3. What are the steps to perform a 90-degree rotation of a function around the origin?
4. How do exponential functions behave under transformations like rotation and translation?
5. What is the significance of dilation and how does it affect the graph of a function?

**Tip**: When reflecting a function, always adjust the function's coordinates relative to the line or axis you are reflecting across.

The image contains five different mathematical transformation problems, each with different functions (linear, absolute, quadratic, exponential, piecewise) undergoing transformations such as translation, rotation, reflection, dilation, and combinations of these. The user is asked to find the transformed values for specific inputs.

Learn how to solve transformations such as translation, reflection, rotation, and dilation on linear, quadratic, exponential, and piecewise functions. This comprehensive breakdown covers detailed steps for each transformation type. Ideal for students in Grades 11-12.

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