2.7 Piecewise Functions

What is a Piecewise Function?•A function that combines pieces of different equations.•Each piece is for a different domain (set of x values).• Example:

Why Are They Important?•In real life, lots of problems are modeled by piecewise functions.•Examples:▫Finding shipping costs▫Income taxes▫Ordering t-shirts

Examples:

Writing Piecewise Functions

•We know how to graph, now go backwards!

•First, find the domains (where the graph is cut)

•Then, find the slopes and y-intercepts.•Fill in the equation for each domain.•Example:

___ x + ___ , if x ______

___ x + ___ , if x ______

Example:

___ x + ___ , if x ______

___ x + ___ , if x ______

Your Turn!

___ x + ___ , if x ______

___ x + ___ , if x ______

Evaluating from a Graph•Move left/right to the x you need, then move up/down to find y.

•Example:•Evaluate f(x) for the function shown when:

•x = -3•x = -1•x = 2

Your Turn!•Evaluate f(x) for the function shown when:

•x = -1•x = 1•x = 2•x = 4

Evaluating Piecewise Functions•The domain tells you which equation to use.

•Evaluate f(x) when:a)x = 0b)x = 2c)x = 4

Your Turn!

•Evaluate f(x) when:•x = 0•x = 3•x = 6

Step Functions

Each piece of the function is a flat, horizontal line.