To assist you effectively, I would need specific equations, graphs, key features, transformations, and the corresponding table of values for the functions you mentioned. Once you provide those details, I can help you match everything accordingly.
However, I can give you a general example of how to analyze functions based on their equations, transformations, and corresponding values.
Example
1. Parent Function: \( f(x) = x^2 \) (Quadratic Function)
2. Transformation: \( g(x) = (x - 2)^2 + 3 \)
- This represents a horizontal shift to the right by 2 units and a vertical shift upwards by 3 units.
3. Key Features:
- Vertex at (2, 3)
- Opens upwards
- Axis of symmetry at \( x = 2 \)
4. Table of Values:
| x | g(x) | |-----|-------| | 0 | 7 | | 1 | 6 | | 2 | 3 | | 3 | 4 | | 4 | 7 |
Matching:
- Equation: \( g(x) = (x - 2)^2 + 3 \)
- Graph: A parabola that opens upwards with vertex at (2, 3).
- Key Features: Vertex, axis of symmetry, and direction of opening.
- Transformation: Horizontal shift right and vertical shift upwards.
If you provide specific functions or data, I'd be happy to walk through the matching process with those details!