It seems like you're asking for assistance in matching various elements related to functions, such as equations, graphs, key features, and transformations. Given that I cannot see the actual graphs, equations, or table of values, I'll guide you through the general process of how to make these matches typically.
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Equation: This will usually be in the form of a function, such as \( y = ax^2 + bx + c \) for a quadratic, or \( y = mx + b \) for a linear function. Identify the type of function based on the equation.
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Graph: Look for the visual representation of the function in the provided options. A key aspect here is whether the graph is parabolic (for quadratics), linear (for lines), or perhaps exponential, etc.
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Key Features: These could include the vertex (for quadratics), intercepts (both x and y), asymptotes (for rational functions), or points of inflection. Determine which features are crucial to the function you are analyzing.
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Transformation: This refers to how the function has changed from its parent function. Common transformations include shifts (up/down/left/right), reflections (over the x or y axis), and stretches or compressions (which affect the steepness of the graph).
Steps to Match:
- Start with the equation: Identify the type and form of the equation and then look for its corresponding graph.
- Look at the graph: Make sure it matches the expected features based on the equation's type.
- Identify key features: Match any special points or characteristics that would help define the function type.
- Determine transformations: Compare the equation to its parent function to see how it has been manipulated.
If you provide specific equations, graphs, or characteristics, I can help with more detailed matches!