Question

What function family does this graph represent?
Responses

Absolute Value
Absolute Value

Cubic
Cubic

Linear
Linear

Quadratic

Answer 1

To determine which function family a graph represents, you would typically look for specific characteristics of each type of function. Here are the key features for each type:

1. **Absolute Value**: The graph forms a "V" shape with a pointed vertex. It is non-negative and symmetric about the vertical line through the vertex.

2. **Cubic**: The graph can have a "wave" shape, usually featuring an S or an inverted S. It can have one or two turning points and is symmetric in a unique way around inflection points.

3. **Linear**: The graph is a straight line, which can have a positive, negative, or zero slope. There are no curves or bends.

4. **Quadratic**: The graph is a parabola, which can open upwards or downwards. It has a vertex as the highest or lowest point and is symmetric about a vertical line through the vertex.

If you can describe the features of the graph you are analyzing, I can help you determine which function family it corresponds to. If it has a "V" shape, it is absolute value. If it resembles a curved parabola, it is quadratic. If it is a straight line, it is linear. Finally, if it has the S-shaped curve, it is cubic.