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Piecewise Functions quiz #1

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  • What is a piecewise function, and how do you evaluate it at a specific value of x?
    A piecewise function is defined by multiple equations, each applying to a specific interval of x values. To evaluate it at a specific x, determine which interval x falls into and substitute x into the corresponding equation.
  • What is a piecewise function?
    A piecewise function is a function defined by multiple equations, each applying to a specific interval of x values.
  • How do you determine which equation to use when evaluating a piecewise function at a specific x value?
    You determine which interval the x value falls into and use the corresponding equation for that interval.
  • What is the first step in graphing a piecewise function?
    The first step is to identify the boundaries where the equations change, often marked by specific x values.
  • How do you represent the boundary point on a graph if the interval does not include the boundary value?
    You use an open circle at the boundary point to indicate that the value is not included in that piece.
  • What does a solid circle at a boundary point on a piecewise function graph indicate?
    A solid circle indicates that the boundary value is included in that piece of the function.
  • What is a jump discontinuity in a piecewise function?
    A jump discontinuity occurs when the y-values of the pieces do not match at a boundary, causing a 'jump' in the graph.
  • How would you evaluate f(-3) for a piecewise function defined as f(x) = -x for x < -1 and f(x) = x^2 - 4 for x ≥ -1?
    Since -3 < -1, use f(x) = -x, so f(-3) = -(-3) = 3.
  • How do you evaluate f(-1) for the same piecewise function?
    Since -1 ≥ -1, use f(x) = x^2 - 4, so f(-1) = (-1)^2 - 4 = 1 - 4 = -3.
  • Why is it important to avoid overlap between the intervals in a piecewise function?
    Overlapping intervals would make it unclear which equation to use for certain x values, so each x should belong to only one interval.