Unit 7

Transformations and Graphs

100

Identify whether the function, f(x)= 5(2/3)^x  represents exponential growth or exponential decay and explain why?

problem 1

decay, 2/3 < 1

200

For f(x)=3^x+1 -6 list domain, range, asymptote, y-intercept, and end behavior

Problem 3

domain: all real numbers

range: y>-6

asymptote: y=-6 

y-intercept: (0,-3) 

end behavior: x-> infinity, f(x) -> infinity

x-> - infinity, f(x) -> -6

300

given f(x) = (1/2)^x-5+2, determine the transformations and given asymptote and range 

problem 4

right 5, up 2, asymptote y=2, range y>2

400

given points for the graph of y=log₂x-3. state range, domain, asymptote, and x-intercept

problem 5

domain x>0 

range all real numbers

asymptote x=0

x-intercept (8,0)

500

Find the domain, range, end behavior, x-intercept, and asymptote for f(x)=log_1/3(x+2)+1 and graph 

problem 6 

domain x>-2

range all real numbers

end behavior x-> -2 f(x)-> infinity

x-> infinity f(x) -> - infinity

x-intercept (1,0)

asymptote x=-2 

Forms and Conversions

100

write 8²=64 in logarithmic form 

problem 7

log₈64=2

200

convert 2^x-4=32 in logarithmic form 

Problem 8

log₂ 32 = x-4

300

write ln x = 38 in exponential form 

problem 14

e³⁸=x

400

convert e⁶=x-2 into logarithmic form and name logarithm used

problem 10

ln x-2 = 6 

natural log

500

solve 10^2x =54 

problem 9

log 54 = 2x

2x=log 54 / log 10 

x=0.8661

Logarithm Skills

100

evaluate log₉81

problem 15

2

200

evaluate log₈₁3

problem 16

1/4

300

solve log₂78=x 

problem 21

x=log 78 / log 2 

x=6.2854

400

evaluate ln 42 

problem 22

3.7377

500

log₇95 = x 

problem 20

x=2.3402

Properties of Logs

100

condense 3 log 2 + log (x-4) 

problem 23

log 8(x-4)

log 8x-32 

200

condense 1/2 log₅ 324- log₅ 2

problem 24

log₅ 9

300

expand and simplify 

log₃ (x²y⁵)³

problem 26

6 log₃x + 15 log₃y

400

expand ln (2/a³)⁴

problem 27

4 ln 2 - 12 ln a 

500

solve for y (extraneous)

2 log (y+5) = log 20 - log 5 

problem 32

y = -3 

Applications

100

problem 41 

171334 birds 

200

problem 42

$2284.79

300

problem 43

$3763.31

400

Problem 44

$18366.78

500

Problem 45

5.2896