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FIU - Study Guide - Midterm

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MgC 1140 Test 3 Notes

Chapter 4 Isection 4.1: Exponential Functions * Exponential function with base b:FX= b

lahere b>0 and bzl and x is any real number. INOT exponential: H(x)=(-1* negative base. Graphing an exponential function

f(x)= 2*

FC :2* Horizontal

asymptotca

V=O We also discuss several other topics like What is teshik, tash?

f(x)= (3)

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y=C2)

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Abdouniis

Characteristics of Exponential Functions of f(x)=b*

We also discuss several other topics like When was the first civil war in rome?

Domain: (00.00) Range: (0,0) © Always pass through (0,1). Yinti L x int: NLA 3 IF b> I graph goes up right. Ine greater the

value of br the steeper the increase IF O<b<l, graph goes down right. The smaller the b Valven the Steeper the decrease © ECx=b is one-to-one and has an invere We also discuss several other topics like Divergent validity is demonstrated by using, what?

Graph of f(x)=b* approaches x-axis but never touches it. Y=0 is horizontal asymptote. tilans formations of exponential functions. ola(x)=b* + C up c units

e down cunits

is up

lar: b*+

C left C units SL =bX-C

right c units

right c units C E-b* reflect about x axis r = b* reflect a bOUE Y-axis Ja (x)=Cbx vertically stretch if C>L If you want to learn more check out What is the importance of dna?

vertically shrink if 0204 Jacx)= 6C* horizontál shrink if (>1 We also discuss several other topics like What are the similar characteristics of the earth’s moon and mercury?

horizontal stretch If 0.404 Natural Base e Te ř2.7218 >section 42: Logarithmic Functions

The inverse function of the exponential function with base bis called the logarithm function with base be

• y: 1096 X is equal to box We also discuss several other topics like How does magma move?

Logarithmic function exponential function

• Example: 109749_7? - 49 72. - 49

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BASIC Logarithmic Properties 1. Jogo b = 1 because bi=b 2. Logn 1 = 0 because bo=1 mverve properties of Logarithms Llog obx=x Ingur = x Find inverse Of F(x) = b

o y = b

© VETOGbX

@ 1(x)= 1096 x Graphs Of Exponential and Logarithmic Function

na i

F(x)=bit

f(x) 6 (0)

f'(x) = logo

F '(x)=109bX

o ba 1 Icharacteristics Of Logarithmic Functions f(x) = logit To Domain: (0.00) Range: (-0.00)

© All logarithmic functions pass through (110) + X-int: 1 yint: N/A

3 If b> graph goes up to right GIF 02b4 graph goes down rights

Graph approaches but doesn't touch y-axis.

X=0 is vertical asymptote. Jorder of transformations.

O Horizontal translation Avertical strech compra 2 Horizontal stretch /compress reflect about X-axis

reflect about y-axis

shift up or down.

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Transformations involving logarithmic functions sur f(x) = logbx+c up c units LETogo X-C down Cunits g(x-logb(xro) left cunits vertical asympt: X=-C

cunirs verrical asymeti X=0 g(x) = -logo x reflect about x-axis

- 10967-x) reflect abouty-axls

K vertical stretch if c>lishrink if OLC4

(cx) horizontal shrink if c>1, stretch IF occ</ properties of common Logarithms

General Properties. common Logarithms

O logo l=0

010g1=0 Blogu b=

0 109 10 = 1 logo b*= x

☺ 109 10x = x @ blogex = x

9 1010gx = x Norural logarithmic function

f(x) = logex = f(x)=Inx Finding domains of natural 10g functions

f(x)= in (3-X) 3-X>0 = (-00,3) > h(x) = n(x-3)2 = (-Do ) U (3,00) Properties of Natural Logarithms

General Properties Natural Logarithms 1 logo1=0

0 101=0 © logo b= 1

@ ine=1 ☺ loqnbx=x

☺ ine* = x blog bx = X

2 einx= x Section 4.3: Properties of Loganthms *

• Product Rule: Togb(MN)= 1096 M + 109 N.

• Quo tient Rule: 10gb ( R ) = logo M-logoN

• Power Rule: 1096 MP = plogo M

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