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
FC :2* Horizontal
V=O We also discuss several other topics like What is teshik, tash?
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
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
) Study Soup
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
@ 1(x)= 1096 x Graphs Of Exponential and Logarithmic Function
f(x) 6 (0)
f'(x) = logo
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.
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