Piecewise functions
A function can use one formula for some inputs and another formula for the rest. How do you read one, draw one and build one?
Where you are 4 inside
What this area is about
A piecewise function is written as several formulas, each paired with a condition on the input, such as x < 1 or x \ge 1. The conditions do not overlap, so each input in the domain is handed to exactly one formula and gets exactly one output. Every skill in this area starts by finding the formula in charge.
How these fit together
From formulas to values and pictures. Evaluating a piecewise function picks the piece whose condition the input meets and uses only that formula. Graphing a piecewise function draws each piece only over its own inputs, and shows whether the graph joins up or jumps where the formula changes.
From a picture back to formulas. Writing the formulas from a graph finds the equation of each piece and the interval of inputs it covers.
Applications. Piecewise functions in context builds one from a threshold in words, such as overtime pay or shipping by weight band, and says what happens exactly at the threshold.
A path through it
The order is fixed: evaluate, then graph, then write the formulas from a graph, then context.
Next: the absolute value graph and step functions, both piecewise functions in disguise, and later making a piecewise function continuous.