= 3 2x 4 +5 - dublin.k12.ca.us Log...2. Graph f(x) = log 3 (x+1) 6 Be sure you can identify:...

1. Graph

y = 3 · 2x−4 + 5Be sure you can identify:Horizontal ShiftVertical ShiftDomain and RangeReflectionAsymptoteY-InterceptX-Intercept

Graph

y = 3 · 2x−4 + 5

−5 −4 −3 −2 −1 1 2 3 4 5

1

2

3

4

5

6

7

8

9

10

Horizontal Shift: right 4 Vertical Shift: up 5Domain RRange y>5Reflection: No Asymptote: y=5

Y-Intercept (0, 53

16) X-Intercept: none

2. Graph

f (x) = − log3(x + 1)− 6Be sure you can identify:Horizontal ShiftVertical ShiftDomain and RangeReflectionAsymptoteY-InterceptX-Intercept

Graph

f(x) = − log3(x+ 1)− 6

−3 −2 −1 1 2 3 4 5

−8−7−6−5−4−3−2−1

1

2

Horizontal Shift: left 1 Vertical Shift: down 6Domain x>-1 Range RReflection: Yes Asymptote: x=-1

Y-Intercept (0, -6) X-Intercept: (−728

729, 0)

3. Evaluate each log below

A. log31

81B. log16 2

C. log7 1 D. logx 125 = 3

E. ln e7 F. log8 16

G. log5 0

Evaluate each log below

A. -4 B.1

4.

C. 0 D. 5

.

E. 7 F.4

3G. Undefined

4. Evaluate

Given log7 4 = .712 log7 3 = .565

.

A. log7 48 B. log79

4C. log7 28

Evaluate

Given log7 4 = .712 log7 3 = .565

.

A. log7(423) = 2(.712) + .565 = 1.989

B. log79

4= 2(.565)− .712 =.418

C. log7 28 = log7(7 · 4) = 1 + .712 =1.712

5. Graph

y = −2 ·(1

3

)x+1

− 4

Identify:Horizontal ShiftVertical ShiftDomain and RangeReflectionAsymptoteY-InterceptX-Intercept

Graph

y = −2 ·(1

3

)x+1

− 4

−5 −4 −3 −2 −1 1 2 3 4 5

−9−8−7−6−5−4−3−2−1

1

Horizontal Shift: left 1 Vertical Shift: down 4Domain R Range y<-4Reflection: Yes Asymptote: y=-4

Y-Intercept (0, −423

) X-Intercept: none

6. Graph

f (x) = 3 log4(x− 2) + 1Be sure you can identify:Horizontal ShiftVertical ShiftDomain and RangeReflectionAsymptoteY-InterceptX-Intercept

Graph

f(x) = 3 log4(x− 2) + 1

−1 1 2 3 4 5 6 7

−5−4−3−2−1

1

2

3

4

5

Horizontal Shift:right 2 Vertical Shift: up 1Domain x>2 Range RReflection: No Asymptote: x=2

Y-Intercept none X-Intercept: (2 +13√4

, 0)

7. Find the inverse of the function

A. f (x) = 3x+9 − 8

B. g(x) = log5(x + 12) + 13

Find the inverse of the function

A. f−1(x) = log3(x + 8)− 9

B. g−1(x) = 5x−13 − 12

8. Condense

A. 2 lnx + 3 lnm− 4 ln 6

B. 4 log6 x− 12 log6 y + log6 9− 3 log6 b

C. ln(x + 5) + ln(x− 5)− ln 3

Condense

A. ln x2m3

64

B. log69x4

b3√y

C. lnx2 − 25

3

9. Expand

A. log4

(3 · 56 · x2

10y3

).

B. ln 20a5 3√bc

.

C. log9

√x3y

18

Expand

A. log4 3 + 6 log4 5 + 2 log4 x− log4 2− log4 5− 3 log4 y

B. ln 20 + 5 ln a+3

2ln b+ ln c

C.3

2log9 x+ log9 y − log9 2− 1

10. Word Problems!

A. You deposit $1200 in a bank account that pays a 3%interest. Find the balance of your account in 10 years. Whenwill you have $2400?B. A radioactive element decays at a rate of 10% per year.Initially there are 1000 grams present. How many grams willremain in 90 years? After how much time will there be 10grams present?C. The loudness of sound is measured by the formulaL = 10 log i where L is the loudness that the ear hears and i isthe intensity of the sound wave. A whisper has an intensity of100 and a normal talking has an intensity of 1,000,000.Calculate how many times louder than a whisper a normalconversation is.

Word Problems!

A. y = 1200(1.03)10 = $1612.702400 = 1200(1.03)t t = 23.4 years =>24 years.B. y = 1000(.9)90 = .076 grams10 = 1000(.9)t log. 9.01= t = 43.71 years.C. Whisper L = 10 log 100 = 20Conversation L = 10 log 1000000 = 603 times as loud.

11. Solve

A. 3e5x−1 + 4 = 37

.

B. 162x+3 = 322x+4

Solve

A. 5x− 1 = ln 11 x = .68

.

B. 28x+12 = 210x+20 x = -4

12. Solve

A. log5(x + 3) + log5(x + 3) = 2

.

B.3

2log8(2x + 1)− 1 = 2

Solve

A. x2 + 6x + 9 = 25 x = 2

B. log8 2x + 1 = 2 x = 31.5

13. Graph

y = −4 ·(1

2

)x+1

− 2

Be sure you can identify:Horizontal ShiftVertical ShiftDomain and RangeReflectionAsymptoteY-InterceptX-Intercept

Graph

y = −4 ·(1

2

)x+1

− 2

−5 −4 −3 −2 −1 1 2 3 4 5

−8−7−6−5−4−3−2−1

1

2

Horizontal Shift: -1 Vertical Shift: -2Domain R Range y>-2Reflection: Yes Asymptote: y=-2Y-Intercept (0, 0) X-Intercept: (0, 0)

14. Graph

f (x) = 2 ln(x− 5)− 3Be sure you can identify:Horizontal ShiftVertical ShiftDomain and RangeReflectionAsymptoteY-InterceptX-Intercept

Graph

f(x) = 2 ln(x− 5)− 3

1 2 3 4 5 6 7 8 9 10

−8

−7

−6

−5

−4

−3

−2

−1

1

Horizontal Shift: 5 Vertical Shift: -3Domain x>5 Range RReflection: No Asymptote: x=5Y-Intercept none X-Intercept: (-.518, 0)

15. Simplify

A. e2x(1− 5e3x)

.

B.2e3

10e4xe2.

C. 6e8x(2e−5x)2

Simplify

A. e2x − 5e5x

.

B.e1−4x

5.

C.24

e2x