HPC2.4 – Library of Functions;

Piecewise-Defined FunctionsLearning Targets:

-Graph the “library of functions”-Graph piecewise-defined functions

Please use your books to fill in the “Library of Functions” sheet.

Linear Function

Domain:

Range:

( )f x mx b

( , )

( , )

Constant Function

Domain:

*Range:

( ) , where isa real numberf x b b

( , )

{ | }y y b

Identity Function

Domain:

Range:

( )f x x

( , )

( , )

Square Function

Domain:

*Range:

2( )f x x

( , )

[0, )

Cube Function

Domain:

Range:

3( )f x x

( , )

( , )

Square Root Function

*Domain:

*Range:

( )f x x

[0, )

[0, )

Reciprocal Function

*Domain:

*Range:

1( )f xx

( ,0) and (0, )

( ,0) and (0, )

Absolute Value Function

Domain:

*Range:

( )f x x

( , )

[0, )

Greatest-Integer Function

Domain:

*Range:

( ) [ ] int( )f x x x x

( , )

| is an integerx x

Piecewise-Defined Functions• When functions are defined by more than one equation.• Certain pieces (equations) are valid for certain x’s. • Each piece (equation) can be any of the functions from the library of

functions.

a) f(-1) =

b) f(1) =

c) f(3) =

d) Domain =

e) Sketch the graph

3, 2 1( ) 3, 1

3, 1

x xf x x

x x

Ex 1)

Ex 2) An economy car rented in Florida from Good Car Rental on a weekly basis costs $91 per week. Extra days cost $23/day until the day rate exceeds the weekly rate, in which case the

weekly rate applies. Find the cost C of renting an economy car as a piecewise function of the number x of days used, where 7≤ x ≤14.

* Any part of a day counts as a full day.

Ex 3) The graph of a piecewise-defined function is given. Write a definition for the graph.