Lesson 13: Exponential and Logarithmic Functions

f Cx 2K exponentTbose

Domain Goo 7 IRRange 0 7Asymptotes y o

Intercepts o Dwhat happens when we

multiply by a constant

9 2

9 5 2

Exponential functions

y c b c BERb o

y intercept ga

ffxt c.bey intercept 0,2

t.EEorEJ

10 2.15IT5 b

ffxk2

Logarithmic FunctionsIf b o b 1 1 then we definethe logarithm in base as

y ogbX faudoulyif b X

4 109,81 b 3 109,04000

d X 1 17 d 7 a 10 53special bases means logoXE 2.718 means logeX

W se

a logs lb _y b logs125 929 16 59 1259 4 y 310 467 4 logs125 3

c log 1 9 d logy 4 y139 1 49 4y o 9 1

109,31 0 10944 1

e log toooo _log o toooo4

f log6.001 g In 67log o 0.001 Y loge y109 0.001 eY e7y 3 9 7

log 0001 3

h log yy x

B by X

logs 5 X

Logarithm as inverse function

y 2

µIfit one

to one Yesfhas an inversefunction

Y 2x

n

verticalasymptoteX o

replace x

withx 3

y 1092X

y lo92