The problem involves understanding and sketching graphs based on the given conditions.

Problem Summary:

1. Given Function: $y = g(x)$ (part of the graph is shown).
2. Key Points: The function has stationary points at $x = 1$ and $x = 3$, and this is reflected in the graph provided.
3. Tasks:
   • Sketch the graph of the related functions:
     • $y = g(-x) + 2$
     • $y = -g(x - 1)$

Solution Steps:

1. Understanding Transformations:

• $y = g(-x) + 2$:

  • Reflection: The function is reflected across the y-axis due to the $g(-x)$.
  • Vertical Shift: The entire graph is shifted 2 units up due to the $+2$.

• $y = -g(x - 1)$:

  • Horizontal Shift: The function is shifted 1 unit to the right due to the $(x - 1)$.
  • Reflection: The function is reflected across the x-axis due to the $-g(x)$.

2. Sketching the Graphs:

• $y = g(-x) + 2$:

  • Start by reflecting the original graph across the y-axis.
  • Then, shift the entire graph 2 units upwards.

• $y = -g(x - 1)$:

  • Start by shifting the original graph 1 unit to the right.
  • Then, reflect the graph across the x-axis.

Graph Sketches:

• For $y = g(-x) + 2$:

  • Reflect the graph horizontally and then move it up.
  • The stationary points that were originally at $x = 1$ and $x = 3$ would now be at $x = -1$ and $x = -3$ respectively, and their $y$-coordinates would be increased by 2.

• For $y = -g(x - 1)$:

  • Shift the graph 1 unit to the right, then reflect it vertically.
  • The stationary points that were originally at $x = 1$ and $x = 3$ would be moved to $x = 2$ and $x = 4$ respectively, with their $y$-coordinates being inverted.

These transformations can be applied step by step to ensure that the graphs are accurately sketched.

Would you like the specific graph sketch details for these transformations?