Graph each piecewise-defined function. f(x)={ -(1)/(2) x^2+2 if x ≤ 2 (1)/(2) x

step 1 In this problem, we need to remember that when we draw a piecewise graph, then we choose the def

Graph each piecewise-defined function. f(x)={ -(1)/(2)...

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Key Concepts

Piecewise-Defined Functions

Piecewise-defined functions are functions that have different expressions or formulas for different parts of their domain. They require careful identification of each domain segment and the corresponding rule, making it important to understand how the function behaves in different intervals.

Graphing Techniques for Piecewise Functions

Graphing piecewise functions involves plotting each part of the function separately according to its specific formula and domain, ensuring that endpoints are properly marked and any open or closed circles are used to indicate whether a point is included or excluded. This technique is essential for accurately representing the entire function.

Quadratic Functions

Quadratic functions are polynomial functions of degree two that typically produce parabolic graphs. Understanding their shape, direction (opening upward or downward), and vertex properties is key when graphing any segment of a piecewise function that is defined by a quadratic expression.

Linear Functions

Linear functions are first-degree polynomial functions with constant rate of change, represented geometrically by straight lines. Recognizing their slope and intercepts is crucial when graphing segments of a piecewise function that are defined by linear expressions.

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