https://file.aiquickdraw.com/mathbot/file/1728568927589ugutu61r.jpg

The inequality shown in the image is \( y < |x| + 3 \). Here's how this inequality can be interpreted and graphed:

### Step-by-step Analysis:

1. **Absolute Value Function**: The equation \( y = |x| + 3 \) represents a V-shaped graph, with the vertex at \( (0, 3) \), and the arms of the "V" have slopes of \( +1 \) and \( -1 \) respectively. This is the boundary line of the inequality.

2. **Inequality \( y < |x| + 3 \)**:
   - The inequality \( y < |x| + 3 \) means we are interested in the region *below* the V-shaped curve. This is because the inequality symbol is "<", not "≤".
   - The boundary \( y = |x| + 3 \) is not included, so the line itself is dashed to indicate that points on this line do not satisfy the inequality.

3. **Graphing**:
   - Draw the V-shaped graph for \( y = |x| + 3 \) with a dashed line.
   - Shade the region *below* this V, because the inequality is \( y < |x| + 3 \).

### Verification with the Image:
From the image, the graph shows a V-shape with a dashed line, and the arrows point downward, indicating that the region below the V is the solution, which is correct based on the inequality.

Would you like more details on how to handle absolute value inequalities, or do you have any specific questions?

### Questions to consider:
1. How would the graph change if the inequality was \( y \leq |x| + 3 \)?
2. What if the equation was \( y > |x| + 3 \)? How would you graph it?
3. Can you identify the vertex of any general equation \( y = |x| + c \)?
4. How do you solve absolute value inequalities algebraically?
5. What are some real-life applications of absolute value functions?

### Tip:
Remember, the inequality symbol determines whether you shade *above* or *below* the graph. If it's "<" or ">", shade below or above respectively.

This guide explains how to graph the inequality y < |x| + 3, focusing on absolute value functions, graphing inequalities, and shading the correct region. Suitable for students in Grades 9-11.

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