= 3 2x 4 +5 - dublin.k12.ca.us Log...2. Graph f(x) = log 3 (x+1) 6 Be sure you can identify:...
Transcript of = 3 2x 4 +5 - dublin.k12.ca.us Log...2. Graph f(x) = log 3 (x+1) 6 Be sure you can identify:...
![Page 1: = 3 2x 4 +5 - dublin.k12.ca.us Log...2. Graph f(x) = log 3 (x+1) 6 Be sure you can identify: Horizontal Shift Vertical Shift Domain and Range Re ection Asymptote Y-Intercept X-Intercept](https://reader030.fdocuments.net/reader030/viewer/2022040623/5d4c0eb988c99342768bcd58/html5/thumbnails/1.jpg)
1. Graph
y = 3 · 2x−4 + 5Be sure you can identify:Horizontal ShiftVertical ShiftDomain and RangeReflectionAsymptoteY-InterceptX-Intercept
![Page 2: = 3 2x 4 +5 - dublin.k12.ca.us Log...2. Graph f(x) = log 3 (x+1) 6 Be sure you can identify: Horizontal Shift Vertical Shift Domain and Range Re ection Asymptote Y-Intercept X-Intercept](https://reader030.fdocuments.net/reader030/viewer/2022040623/5d4c0eb988c99342768bcd58/html5/thumbnails/2.jpg)
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
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2. Graph
f (x) = − log3(x + 1)− 6Be sure you can identify:Horizontal ShiftVertical ShiftDomain and RangeReflectionAsymptoteY-InterceptX-Intercept
![Page 4: = 3 2x 4 +5 - dublin.k12.ca.us Log...2. Graph f(x) = log 3 (x+1) 6 Be sure you can identify: Horizontal Shift Vertical Shift Domain and Range Re ection Asymptote Y-Intercept X-Intercept](https://reader030.fdocuments.net/reader030/viewer/2022040623/5d4c0eb988c99342768bcd58/html5/thumbnails/4.jpg)
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)
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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
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Evaluate each log below
A. -4 B.1
4.
C. 0 D. 5
.
E. 7 F.4
3G. Undefined
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4. Evaluate
Given log7 4 = .712 log7 3 = .565
.
A. log7 48 B. log79
4C. log7 28
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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
![Page 9: = 3 2x 4 +5 - dublin.k12.ca.us Log...2. Graph f(x) = log 3 (x+1) 6 Be sure you can identify: Horizontal Shift Vertical Shift Domain and Range Re ection Asymptote Y-Intercept X-Intercept](https://reader030.fdocuments.net/reader030/viewer/2022040623/5d4c0eb988c99342768bcd58/html5/thumbnails/9.jpg)
5. Graph
y = −2 ·(1
3
)x+1
− 4
Identify:Horizontal ShiftVertical ShiftDomain and RangeReflectionAsymptoteY-InterceptX-Intercept
![Page 10: = 3 2x 4 +5 - dublin.k12.ca.us Log...2. Graph f(x) = log 3 (x+1) 6 Be sure you can identify: Horizontal Shift Vertical Shift Domain and Range Re ection Asymptote Y-Intercept X-Intercept](https://reader030.fdocuments.net/reader030/viewer/2022040623/5d4c0eb988c99342768bcd58/html5/thumbnails/10.jpg)
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
![Page 11: = 3 2x 4 +5 - dublin.k12.ca.us Log...2. Graph f(x) = log 3 (x+1) 6 Be sure you can identify: Horizontal Shift Vertical Shift Domain and Range Re ection Asymptote Y-Intercept X-Intercept](https://reader030.fdocuments.net/reader030/viewer/2022040623/5d4c0eb988c99342768bcd58/html5/thumbnails/11.jpg)
6. Graph
f (x) = 3 log4(x− 2) + 1Be sure you can identify:Horizontal ShiftVertical ShiftDomain and RangeReflectionAsymptoteY-InterceptX-Intercept
![Page 12: = 3 2x 4 +5 - dublin.k12.ca.us Log...2. Graph f(x) = log 3 (x+1) 6 Be sure you can identify: Horizontal Shift Vertical Shift Domain and Range Re ection Asymptote Y-Intercept X-Intercept](https://reader030.fdocuments.net/reader030/viewer/2022040623/5d4c0eb988c99342768bcd58/html5/thumbnails/12.jpg)
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)
![Page 13: = 3 2x 4 +5 - dublin.k12.ca.us Log...2. Graph f(x) = log 3 (x+1) 6 Be sure you can identify: Horizontal Shift Vertical Shift Domain and Range Re ection Asymptote Y-Intercept X-Intercept](https://reader030.fdocuments.net/reader030/viewer/2022040623/5d4c0eb988c99342768bcd58/html5/thumbnails/13.jpg)
7. Find the inverse of the function
A. f (x) = 3x+9 − 8
B. g(x) = log5(x + 12) + 13
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Find the inverse of the function
A. f−1(x) = log3(x + 8)− 9
B. g−1(x) = 5x−13 − 12
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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
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Condense
A. ln x2m3
64
B. log69x4
b3√y
C. lnx2 − 25
3
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9. Expand
A. log4
(3 · 56 · x2
10y3
).
B. ln 20a5 3√bc
.
C. log9
√x3y
18
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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
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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.
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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.
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11. Solve
A. 3e5x−1 + 4 = 37
.
B. 162x+3 = 322x+4
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Solve
A. 5x− 1 = ln 11 x = .68
.
B. 28x+12 = 210x+20 x = -4
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12. Solve
A. log5(x + 3) + log5(x + 3) = 2
.
B.3
2log8(2x + 1)− 1 = 2
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Solve
A. x2 + 6x + 9 = 25 x = 2
B. log8 2x + 1 = 2 x = 31.5
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13. Graph
y = −4 ·(1
2
)x+1
− 2
Be sure you can identify:Horizontal ShiftVertical ShiftDomain and RangeReflectionAsymptoteY-InterceptX-Intercept
![Page 26: = 3 2x 4 +5 - dublin.k12.ca.us Log...2. Graph f(x) = log 3 (x+1) 6 Be sure you can identify: Horizontal Shift Vertical Shift Domain and Range Re ection Asymptote Y-Intercept X-Intercept](https://reader030.fdocuments.net/reader030/viewer/2022040623/5d4c0eb988c99342768bcd58/html5/thumbnails/26.jpg)
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)
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14. Graph
f (x) = 2 ln(x− 5)− 3Be sure you can identify:Horizontal ShiftVertical ShiftDomain and RangeReflectionAsymptoteY-InterceptX-Intercept
![Page 28: = 3 2x 4 +5 - dublin.k12.ca.us Log...2. Graph f(x) = log 3 (x+1) 6 Be sure you can identify: Horizontal Shift Vertical Shift Domain and Range Re ection Asymptote Y-Intercept X-Intercept](https://reader030.fdocuments.net/reader030/viewer/2022040623/5d4c0eb988c99342768bcd58/html5/thumbnails/28.jpg)
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)
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15. Simplify
A. e2x(1− 5e3x)
.
B.2e3
10e4xe2.
C. 6e8x(2e−5x)2
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Simplify
A. e2x − 5e5x
.
B.e1−4x
5.
C.24
e2x