Graph each piecewise-defined function. f(x)={ 0 if x<0 x^2 if 0 ≤ x ≤ 2

step 1 Here we have, it's going to be zero if it's less than zero. So there we go. That's the first one

Graph each piecewise-defined function. f(x)={ 0 if ...

Key Concepts

Continuity and Endpoint Behavior

When graphing piecewise functions, it is important to determine whether the function is continuous at the points where the pieces meet. This involves assessing left-hand and right-hand limits at the boundary points and deciding if a jump discontinuity or a removable discontinuity exists based on whether endpoints are included or excluded.

Graphing Techniques for Piecewise Functions

Graphing piecewise functions requires plotting each segment of the function over its respective interval. This process involves drawing the curve or line for each segment and making sure that the graph accurately reflects the boundaries defined by the conditional statements, such as using open circles for excluded endpoints and closed circles for included endpoints.

Domain Partitioning

Domain partitioning involves dividing the function's domain into separate segments based on the conditions provided. Each segment or interval is associated with a specific expression, and understanding these divisions is crucial for correctly applying the appropriate rule.

Piecewise-Defined Functions

A piecewise-defined function is one that is described by different expressions over different intervals of its domain. Each piece applies only over a specified part of the domain, which requires careful consideration when evaluating or graphing the function.

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