The graph shown is a V-shaped graph, characteristic of an absolute value function. The general form of an absolute value function is:

$y = a|x - h| + k$

Where:

• $(h, k)$ is the vertex of the graph.
• $a$ affects the steepness and orientation of the "V".

Step-by-step analysis:

1. Vertex: The vertex of the graph is located at $(-2, -3)$ based on visual inspection.
2. Transformation:
   • The horizontal shift $h$ corresponds to the x-coordinate of the vertex, so $h = -2$.
   • The vertical shift $k$ corresponds to the y-coordinate of the vertex, so $k = -3$.
   • The graph opens upwards, so the coefficient $a = 1$.

Equation form:

Since the vertex is $(-2, -3)$, the equation of the absolute value function is:

$y = |x + 2| - 3$

Looking at the provided answer choices, the correct equation is:

$y - 3 = |x + 2|$

Thus, the correct answer is the second option from the top: $y - 3 = |x + 2|$.

Would you like more details, or do you have any further questions?

Here are some related questions for further practice:

1. What happens to the graph if we change the coefficient $a$ to a number other than 1?
2. How does shifting the graph horizontally or vertically affect the equation?
3. How can you reflect the graph over the x-axis using the equation?
4. What is the equation of the graph if the vertex is at $(3, 4)$?
5. How do you determine the slope of the lines that form the "V" shape in an absolute value graph?

Tip: The vertex form $y = a|x - h| + k$ is very useful for understanding shifts and transformations of absolute value graphs.