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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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