F'unctional

Notation

y

andflx) mea.n the

sa-me thitg.

So are interchangeable.

So, if

you

are

r-ising

the dependent

variable

&),

that

woriid

ntt be functional

notation.

tf, instead of

y.

you

use

f{x). that

would

be

functional notation.

ln the lailer

case.

v

is not

visible.

.7

Example:

y==

x

would

be

regular

notaticn

(dependent

variable notation)

whiie

f(n)*'

wouid

be functional notation.

Example:

The

quantity

of

goods

sold

is

a

function

of

the

price.

If

we let

Q

represent

the

quantrty

&

p

the

price,

we

would

have,

Q={p).

So,

if

the

relationship

is

q=

l00p -

p

2,

we

could

say,

f(p):100p-p',

for functional notaiion.

Hpfkins

Hith

"functiqlul

notatiqn

-Let's

take

g(x):2x'

-x+5.

9(0):2(0)'

-O+5:5, g(

1

)=2(1)'

-l+5:6,

g(h)=Zh'-h+5, g(x+h):2(x+h)'-1*+h;+5

(we

could

simplig

this,

if

needed).

Increasins

and decreasing functions

Igrcrquog.function:

FIas

a

Saph

that

rises

as

x increases.

Show example.

Decreaqing

function: Has

a-graph

that

falls

as x increases.

Show example.

Concavitv

Concave up: Graph

"holds

watet''

(bends

upward).

Show

Cp.nca,ve

down: Graph

"spills water"

(bends

downward).

Show

*The

graph

of

a

function can

have both- The

point

at which

the concavity

changes, is

called a

point

ofjnfectrop"

Show an

example illustrating

all

above...