Piecewise functions
▶ Introduction to piecewise functions
A piecewise function is a function built from pieces of different functions over different intervals. For example, we can make a piecewise function f(x) where f(x) = -9 when -9 < x ≤ -5, f(x) = 6 when -5 < x ≤ -1, and f(x) = -7 when -1
▶ Worked example: evaluating piecewise functions
A piecewise function is a function that is defined in separate "pieces" or intervals. For each region or interval, the function may have a different equation or rule that describes it. We can evaluate piecewise functions (find the value of the function) by using their formulas or their graphs.
▶ Worked example: graphing piecewise functions
A piecewise function is a function that is defined in separate "pieces" or intervals. For each region or interval, the function may have a different equation or rule that describes it. We can graph a piecewise function by graphing each individual piece.
▶ Worked example: domain & range of step function
Finding the domain and range of a piecewise function that is constant in each segment. Such functions are called "step functions."
▶ Worked example: domain & range of piecewise linear functions
Finding the domain and range of a piecewise function where each segment is linear.
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