hpc 2.4 – library of functions; piecewise-defined functions
DESCRIPTION
Please use your books to fill in the “Library of Functions” sheet.TRANSCRIPT
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.