pre lesson 2.1 what is a function? objectives: to review domain. to understand function notation. to...
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PREPRELesson 2.1 What is a Function?
Objectives:• To review domain. • To understand function
notation.• To understand how to
evaluate functions and piecewise functions.
• To understand the difference quotient.
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256289324361400441484529576625676729784841900
1248
163264128256512
Quiz Time
DOMAIN (RECALL)
domain of a function is the values of the independent
variables.1.) ( )9
a f xx
.) ( ) 3 6b f x x
{ 9}x x { 2}x x
FUNCTION F(X) = YA function is a relationship
between
two variables such that each value of
the first variable is paired with exactly
one value of the second variable.
2
1( )1
f xx
Evaluate:
a)f(3)
b)f(-2)
c)f( )5
2
1( )( 1
33)
f
18
2
1( )(
22) 1
f
13
2
1( )( 1
55)
f
14
PIECEWISE FUNCTION
A piecewise function is defined by
different formulas on different parts of
the domain.
Ex 2. A cell phone plan costs $39 a month.• The plan includes 400 free minutes and
charges 20¢ for each additional minute.• The monthly charges are a function of the
number of minutes used, given by
Find C(100), C(400), and C(480)
39 0 400( )
39 0.2( 400) 400if x
C xx if x
(100) $39C (400) $39C (480) $55C
a) f(-5)
b) f(3)
c) f(0)
d) f(1) 2
3 0( ) 1 0 2
2 2
x if xf x x if x
x if x
15
1
1
2
h
Ex 4. Evaluate f(x) = 3x – 1 at the following values.
a) f(a)
b) f(a + h)
c) ( ) ( )f a h f ah
3 1a
)3( 1a h 3 3 1a h
3 1a
( )
3hh
3
( ) ( )f a h f ah
2( ) 2 9f x x
2 22( ) 9 (2 9)a h ah
2 2 22( 2 ) 9 2 9a ah h ah
2 2 22 4 2 9 2 9a ah h ah
24 2ah hh (4 2 )h a h
h
4 2a h
Classwork: Book: pg.155, 14,24,34,44,54,66