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Piecewise Functions definitions

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  • Piecewise Function
    A mathematical rule composed of multiple equations, each applying to a specific interval of the input variable.
  • Interval
    A set of x values for which a particular equation within a function is valid.
  • Boundary
    A value of x where the equation defining a function changes to another equation.
  • Graph
    A visual representation showing how a function behaves across its domain, often highlighting changes at boundaries.
  • Open Circle
    A notation on a graph indicating a point that is not included in the function's domain at a specific boundary.
  • Solid Circle
    A notation on a graph indicating a point that is included in the function's domain at a specific boundary.
  • Jump Discontinuity
    A sudden change in the y value of a function at a boundary, causing the graph to break or 'jump.'
  • Domain
    The complete set of x values for which a function is defined, possibly split among different equations.
  • Equation
    A mathematical expression that defines the output of a function for a given interval of x values.
  • Parabola
    A U-shaped curve on a graph, often representing a quadratic equation within a function.
  • Line
    A straight path on a graph, typically representing a linear equation within a function.
  • Discontinuity
    A point or region where a function is not continuous, often marked by a break or gap in the graph.
  • Continuous Curve
    A graph with no breaks or jumps, where the function's output changes smoothly across its domain.
  • Evaluation
    The process of finding the output of a function by substituting a specific x value into the appropriate equation.