Question

the graph below belongs to which function family?

• linear
• quadratic
• cubic
• absolute value

Explanation:

🆕 New Concept Discovered: Identifying Function Families
Recognizing parent functions by their geometric shapes.

Step 1: Analyze the shape of the graph

The given graph consists of two straight line segments that meet at a single sharp point (a vertex) at the coordinate \( (0, 3) \).

This characteristic "V" shape (or inverted "V" shape) is the signature geometric representation of an absolute value function.

Step 2: Compare with other function families

• Linear functions form a single, continuous straight line with a constant slope throughout.
• Quadratic functions form a smooth, U-shaped curve called a parabola.
• Cubic functions form an S-shaped curve.
• Absolute value functions form a sharp "V" or inverted "V" shape because the slope abruptly changes sign at the vertex.

Since this graph has a sharp peak at \( (0, 3) \) and straight lines extending downward on either side, it belongs to the absolute value function family.

Answer:

absolute value