Terminology
What do you do to check/probe that you have the correct inverse?
Compose the original function and inverse function
Quadratic
Find the inverse using the switch and solve method
y=2x-1
y=(x+1)/2
Convert into exponential form log3x=y
3y=x
If a liquid has a hydrogen concentration of 2.5*10-5 mol/L, what is its pH?
4.6
What does it mean to expand a logarithm?
To take something written as one log, using the log laws, to write it as multiple logs
What is the name of the function y=x3
Cubic
Find the inverse of y=3x2+2
y=sqrt[(x-2)/3]
Expand log(x2y)
2logx+logy
A sound is about 349 times as intense as threshold sound. What is the decibel rating of the sound?
25.4 dB
What does it mean to condense a logarithm?
To take many logarithms, using the log laws, and writing them as one log
What is the name of the function: y=|x|
Absolute Value
Find the inverse of y=2sqrt(x+2)
y=(x/2)2-2
Convert into logarithmic form xy=z
logxz=y
You invest $250 in an account with 8% interest. How much money will you have after 10 years?
$556.38
What are 3 uses of exponential functions in real life?
Compounding interest
Radioactive Decay
Population Growth
Depreciation
Half-Life
What is the domain and range of the square root function?
D: [0,infinity)
R: [0,infinity)
Find the inverse of y=(3x)3-1
y=[cuberoot(x+1)]/3
Condense 2logx+3logy-4logz
logx2y3/z4
A biologist is researching a newly-discovered bacteria. She puts 200 bacteria into a favorable growth medium. 5 hours later, she measures 500 bacteria. What is the growth constant for the bacteria?
0.18
What are 3 uses of logarithms in real life?
pH
Richter Scale for Earthquakes
Sound
What is the domain and range of the exponential function?
D: (-infinity,infinity)
R: (0,infinity)
Find the inverse of y=2*3x
y=log3(x/2)
Write the exponential function from two points
(2,72) and (-1,1/3)
y=2*6x
The half-life of a material is 99 minutes. If you start with 12 g of material, how much will you have after 75 minutes?
7.097 g