Unit 3 Lesson 6 Piecewise functions

Write and equation for each part.

TRWEHSTREH

State the intervals that represent each part.

EFRGHFMEWE

Evaluate each. Is this a linear piecewise function? Justify.

This is not a continuous graph. This is not a linear piecewise function because the 2nd piece is a curve.

A certain cab company has a $2.00 base charge, and then charges $0.50 per minute. There is also a $7.00 minimum fee (so if the base charge and minutes combined don't add to $7, the rider is charged a flat amount of $7). Does the function that describes riding a cab from the company for x minutes and spending f(x) dollars?

Yes it does.

Piecewise defined functions

can take on a variety of forms. Their "pieces" may be all linear, or a combination of functional forms (such as constant, linear, quadratic, cubic, square root, cube root, exponential, etc.). Due to this diversity, there is no "parent function" for piecewise defined functions. Piecewise defined functions may be continuous (as seen in the example above), or they may be discontinuous (having breaks, jumps, or holes as seen in the examples below).

Is the graph a function? Justify.

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Piecewise functions

functions that have multiple pieces, or sections. They are defined piece by piece, with various functions defining each interval. Piecewise functions can be split into as many pieces as necessary. Each piece behaves differently based on the input function for that interval. Pieces may be single points, lines, or curves. The piecewise function below has three pieces.

A step function (or staircase function)

is a piecewise function containing all constant "pieces". The constant pieces are observed across the adjacent intervals of the function, as they change value from one interval to the next. A step function is discontinuous (not continuous). You cannot draw a step function without removing your pencil from your paper.