The graph provided shows a V-shaped curve, which is characteristic of an absolute value function. To determine the equation that represents the graph, we need to analyze a few key features:

1. Vertex of the graph: The vertex of the V-shape appears to be at $(-3, 2)$. This means the absolute value function has been shifted horizontally to the left by 3 units and vertically up by 2 units.

2. Orientation and slope: The graph opens upwards, indicating a positive slope, and there are no reflections.

The general form of an absolute value function is $f(x) = a|x-h| + k$, where:

• $(h, k)$ is the vertex,
• $a$ controls the steepness (which here seems to be 1 since the slopes on either side of the vertex rise at a 45-degree angle).

Step-by-Step Analysis:

• The vertex is $(-3, 2)$, so the equation must involve $|x + 3|$ and a vertical shift by 2 units upwards.
• Thus, the correct equation is $f(x) = |x + 3| + 2$.

Therefore, the correct answer is:

A. $f(x) = |x + 3| + 2$

Would you like more details or have any other questions?

Here are some related questions to deepen your understanding:

1. How would the equation change if the graph opened downwards?
2. What effect does changing the slope value $a$ have on the graph?
3. How would you describe the graph of $f(x) = |x - 3| - 2$?
4. What is the domain and range of the given absolute value function?
5. How would a vertical stretch affect the graph of $f(x)$?

Tip: The vertex form of an absolute value function $f(x) = a|x-h| + k$ allows you to easily identify shifts and transformations of the graph.