Graphs
Solving Exp/ Logs
Condense/ Expand
Transformations
Real World Applications
100
Describe the end behavior of log2(x)-9.
x -> infinity, f(x) -> infinity
x -> 0, f(x) -> -infinity
100
Solve log(x+3) + log(2) = log(4x)
x = 3
100
Expand log(
/ z6)
1/2 log(x) - 6 log(z)
100
Describe the transformations that occurred to f(x)=log3(2x-6)+11
Right 3
Horizontal compress 1/2
Up 11
100
The population of Walzem from 2018-2019 can be represented by the equation P(t)=300e0.23t where t represents the year and t=1 corresponds to 2019. When will the population be equal to 900?
nsolve(900 = 300e0.23t, t) t=4.77 + 2018 = 2023.
200
Describe the end behavior of 2(9)x.
As x -> - infinity, f(x) -> 0
As x -> infinity, f(x) -> infinity
200
Solve log(x-9) + log(2) = log(x)
x =18
200
Simplify (3)log2(2) + log2(2)
a) 2
b) -3
c) 4
d) -4
c) 4
200
Describe the transformation of f(x)=log8(5x+10)-7
Left 2, Horizontal shrink 1/5, down 7
200
The population of people from 2010-2015 can be represented by the equation P(t)=60000e0.03t where t represents the year and t=1 corresponds to 2014. When will the population be equal to 1,000,000?
nsolve(1000000 = 60000e0.03t, t) t=93.7 + 2013 = 2107.
300
Describe the end behavior of (1/8)-x.
As x -> - infinity, f(x) -> 0
As x -> infinity, f(x) -> infinity
300
Solve e2x-6x=16.
ln(8), ln(-2) -> extraneous solution
300
Simplify (3)log3(3) + log3(1)
a) -3
b) 2
c) 3
d) 5
c) 3
300
What is the domain of f(x) = log10(2x-4)?
(2, infinity)
300
Jorge invests $122,000 into an account paying 2.3% annually. How long will it take for the account to reach $160,000 if the interest is compounded 2 times a year?
nsolve(160000 = 122000(1+0.023/2)2t, t)
t = 11.8 years
400
Describe the end behavior of ex+500.
As x -> - infinity, f(x) -> 500
As x -> infinity, f(x) -> infinity
400
Solve 2x+4=16-3
x=-16
400
Expand ln(4/ y13)
(2)ln(x) - (13)ln(y)
400
What is the domain of f(x)=ln(3x-9)?
(3, infinity)
400
I invest $9,000 into an account paying 3.9% annually. How long will it take for the account to reach $12,000 if the interest is compounded monthly?
nsolve(12000 = 9000(1+0.039/12)12t, t)
t = 7.38 years
500
What is true about 3x-9?
A. It is bounded above.
B. There are no local or absolute extrema.
C. The graph is increasing on (-infinity, infinity)
500
Solve 29+x=8-8
x=-33
500
Expand log(3 / z9)
(3/2)log x - (9)log z
500
Describe the end behavior of f(x)=e-3x
As x -> -infinity, f(x) -> infinity
As x -> infinity, f(x) -> 0
500
What is the inverse of f(x)=5x?
a) log5x
b) log10
c) 5 = x
d) log5x
d) log5x