The graph is shifted to the right by 5 units, stretched vertically, and shifted up 12 units.

To analyze how the graph is transformed based on the descriptions provided, let’s break down each transformation and represent the changes mathematically.

1. Break Down the Problem

   • The original function can be denoted as $f(x)$.
   • We need to apply three transformations:
     1. Shift to the right by 5 units.
     2. Stretch vertically (the factor will depend on the specific scenario; we'll denote it as $k$).
     3. Shift up by 12 units.

2. Relevant Concepts

   • Shifting to the right by $a$ units is represented as $f(x - a)$.
   • A vertical stretch by a factor of $k$ is represented as $k \cdot f(x)$.
   • Shifting up by $b$ units is represented as $f(x) + b$.

3. Analysis and Detail

   • Starting with the original function $f(x)$:
     1. Shift right by 5 units: $f(x - 5)$
     2. Stretch vertically: $k \cdot f(x - 5)$
     3. Shift up by 12 units: $k \cdot f(x - 5) + 12$

4. Verify and Summarize

   • Putting it all together, the final transformation of the function can be represented as: $g(x) = k \cdot f(x - 5) + 12$
   • Here, $g(x)$ is the transformed function where $k$ is the vertical stretch factor, which needs to be defined for specific scenarios.

Final Answer

The transformed function is given by: $g(x) = k \cdot f(x - 5) + 12$ where $k$ is the vertical stretching factor.