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UNCC / Math / MATH 1120 / How do you find the domain of a polynomial graph?

# How do you find the domain of a polynomial graph? Description

##### Description: these notes will cover what will be on the first exam.
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## How do you find the domain of a polynomial graph? 2.3: Functions & Mathematical Models Polynomial Functions: punand function of carcen 10). axta xn't taxta x'ta wroce nisa positive cheer Due ce concos

(coned constrients 4x - 3x2+x+2 (degree of 3) 275_3/2x2+4 (coefficients can be any number

## What is a polynomial function of degree? (x2 - 4) 3 (dearce is 6 3x2 - 4xt to -

35 not a polynomal

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2x31x2 + 4x -

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• Domnuin of polynomial functions:

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• Polynomial functions of degree : loco fuoco

SCD= 3-4 If you want to learn more check out What does thermal energy depend on?

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## How do you know a function is rational? • Polynomial Bunctions of degree

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6.346 & 8. Do these equations define vas a linear function of 1? If so, write it in the slope-intercept formi. Don't forget about the age old question of What is it called when you have multiple partners in a relationship?

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3

-6y +7=0

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-64+]=-3x - by 3-7 = 4 = 1/2x+71 If you want to learn more check out What are the vertebrae in the neck region called?

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• Domain of national functions: We also discuss several other topics like Do multicellular bacteria exist?

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3

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m e turer huis monthly fixed out of \$100.000 mod a production cost of \$14 for each unit produced. The products for \$20 per unit.

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(a) What is the cost function?

CO) = 14x + 100,000

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(b) What is the revent function?

RC = P.X = 20x

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(c) What is the profit function? P(x) = R(x) - CEx) = 20

- 20% (14x+100,000)

ELX - 100,000 (d) Compute the profit (or loss) corresponding to production levels of 12,000 and 20,000 units. (12,000)=L(12,000) -100,000

72.000-100000 = -28,000 P(20,000) = (20,000) 100 = \$ 28,000 loss

= 120,000 -100,000 = 20,000 \$20,000 Profit

OI=XZ O=01-26

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(oz+x) (01-X 2) = CO2 + x)01-02 + x2 =

1002-01 x Oht zx 2 = 0 Oi-oh of ooh

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OZ+ Ol+ (92) 10 = OZ EXST 7*70 = Oh O2+(5]Z+CS)10d 02+x2 + 2X2.0= Ohtx O2 + x2+2x10= Onix - 7X10

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X=5

the equilibrium quantity and price.

spectively, where p in mind in dollins F

nd in umiin of hundred. Find

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lim

f(x)=3

y =

)

f(-2)=4

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Where does a function Oil to have a limit?

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lim

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2.4.38:Find lim

+2 =

5(-2)+2 =

1+z =

-8

= -2

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Indeterminate Form

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2.4#52. Find ding 24* =260-3(0)

0

= lim 2x-3

=2(o)-3=-3

x=3 = lim x+2 = 312=5

{-x

(2+x) (EX)

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hex "17=2+2=2+ h = 2+1 wil

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17--2-2-=

5 = ty

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Z-ex

2+x

(2-x) w

Cz+

(2-x) = SP (9+b79-b) = (9-)

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NO o

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col-001

X-oby

50

0.5 (100)

0.56x)

lim

(b) Evaluate lim C(r) and interpret your result.

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9

Sb-00!

Solop van

SYONO VOC

Sb= g Lhobl s'o= (56)

SIDOR Oligh=gh =

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lim 2 = 0

lim t=0

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Technique for evaluate the limitat infinity of a rational function:

divide numerator and denominator by xn whore nis the degree of the denominator

2.4#78: Find lim =

-100 2.1

stud

+1

+1+1

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2.1#78: Find lim 2++= m (4x -3x2+D

= lim 4-3 1/2 + 1/4 00 Lt) (2x + x3 + x2+x+1) X3 (2+\/x+'/x+2+x!

SEU

= lim

o=0

- en walls

be

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4x11x

telo o

lim

4x=0

3x3 + x2 +

3 + x + x2

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@ when numador & beraninator are the Sorre, you will get a ratio of the Coefficient

You should be able to

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• Evaluate limits using graphs.

• Use alegra to evaluate a limit with the indeterminate form.

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Evalunge limits at infinity using graphs and using algelorat.

HOMEWORK, Section 2.4: 1-13 every other odd, 17, 23-31 every other odd, 49, 53, 57, 59, 63, 65, 73-85 odd

-24X

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Cornombors slightly smaller than a) Tas x approaches a from the left

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i nzuri = (175 sa

7+(172 =

tax un= (y wcz

9=(h+(172) = 0

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(f(x) = o) on a certian interval.

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Intermediate Value Theorem:OND IS S

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16=2-2-=(2-x) wn

= (2-) 5

(2-x)(2+x)

dnosapnis

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+

2+ - aX

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un = (y wi= (2-) =

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(D11-

201-6-)

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01 = (122+8

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18-8

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(27-09]} = sobrass+2

average webcity betw.

4-2

Zl=hts = (272 +9 =42+

z [hz]

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2+2'2 utx

(27)-Chahya Rooney

21= 2das

9-25 =

Owen vochty = doce

DOCH Z

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2.0 The Derivative

D 9N40 volouhodou John

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(b) Use the Intermodinte Value Theorem la conclude that the oxygen content of the pond

must have been at a level of 80% at some time. Colo) Where is t2 +204+10o=0?

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01-276o=(01+7) (01+7)

f(t) is continuous on (0,10) because it is continuous everywhere except x=-10 By N.T, the level must have been so lo at some time between ott

To=t (c) At what time(s) is the oxygen content at the 80% level?

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[42+8=

= 8h+ 2h2

8=6.2= 2(2) = (2) 7

A 48+8=

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(87- (242+48

(24+ 42+42+ h) 2 = (4+2)(4+2)2 =

(472)2 = (4+2)

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(297-(4+2) -

on the interval 2,2+HT

What is the average rate of change for our Wunction () = 2

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Average Rate of Change New

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b=148 =(5-0)2+8

go=4 

spuogos

Z= 9

Z

(2) -(92]) SZ=77 =7 07 TA 'JAD

9=(7) 52 = 269 27Z = (52)

the population F= 0. The graph of a gives the population dolajimlar buncitori culture of time after a portion of Elencide was introduced into the population = 0. 1 Which population is decreasing faster 7 B b. Which population is decreasing fastar 7 A

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C. Which bactericide is more effective in reducing the

population of bacteria in the short run? In the long run? - черя, я е, че

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Notation for the derivatives

-f(x) = 2x2

f'(x) = 4x

0.4=2x2

41 =44

dy = 4x

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xh = 70

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xh= (2+2)

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V SOUD

= 23 - (4t 2) 7

1748=(012+8=42+8

way

What is the instantaneous rite of change for our function f(1) = 21 at I=2?

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son of the live traccent to f ct x.

This is the

-(44)

at Six to open op

. Skol DeckOC.

u

Instantaneous Rate of Change: Tercho

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ful sec

= 8.002

L= (275-000 25 100 0=4

10=4 sozy

- (10ozge

Cutzo

K= 2

seconds

(*) 7

(44) J

average velocity

1

272 = (7) J

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