The graph displayed in the image represents a V-shaped function, which typically indicates an absolute value function. In the graph, the vertex appears to be at $(-1, 3)$, and the graph is symmetric around this point.

Now, let's examine the equations to find the one that matches this graph:

• Option 1: $g(x) = |x + 1| + 3$
  This function has a vertex at $(-1, 3)$, which matches the graph's vertex.

• Option 2: $g(x) = |x + 3| - 1$
  This function has a vertex at $(-3, -1)$, which does not match the graph.

• Option 3: $g(x) = |x - 1| + 3$
  This function has a vertex at $(1, 3)$, which does not match the graph.

• Option 4: $g(x) = |x + 3| + 1$
  This function has a vertex at $(-3, 1)$, which does not match the graph.

Thus, the correct equation that represents the graph is:

$g(x) = |x + 1| + 3$.

Would you like more details or clarification on how we arrived at this answer? Here are some follow-up questions you may find useful:

1. What is the general form of the absolute value function?
2. How do you find the vertex of an absolute value function from its equation?
3. How does the coefficient inside the absolute value expression affect the graph?
4. What are the key characteristics of a "V-shaped" graph?
5. How do transformations of the absolute value function affect its graph?

Tip: To identify the vertex of absolute value functions, check the sign and position of the terms inside and outside the absolute value symbols.