Extra 5 point pass if you can solve (and show how)…
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Transcript of Extra 5 point pass if you can solve (and show how)…
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Extra 5 point pass if you can solve (and show how)…
Find the inverse of:
*10 minute limit!!!
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3.2 – Logarithmic Functions and Their Graphs
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Some things to ponder….What are the properties of exponential functions that we learned yesterday?
Who remembers how to determine if a function has an inverse?
Will an exponential function have an inverse?
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y = ax has an inverse logax=y
y = ax is equivalent to logay=x
Remember that logs are exponents…. So logax is the exponent to which “a” must be raised to obtain x
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Ex. 1) log28=?
Ex. 2) log232=?
Ex 3) log10(1/100)=?
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Log4774000=?
55x=22500
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Graphing Logs…
y=logax Domain: (0,∞)
Range: (- ∞, ∞ )
x intercept: (1,0)
increasing: (0, ∞)
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Graph f(x)=log2x
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Graph f(x)=log3x + 4
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Transformations…..f(x)=logbx g(x)= alogb(c(x-h))+k
The transformations are the same for “a”, “c”, “h”, and “k” for all the other functions we have studied….*absolute value, quadratic, exponential, etc.
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Natural Log Function…
f(x)=logex lnx
y=ex and y = lnx are inverses
y=lnx implies ey=x
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Properties…e0=e1=ln ex=elnx=ln(1)=ln(0)=ln(-1)=If lnx = lny then
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Simplify with out a calculator:
(a) ln(b) e ln5
(c) (d) 2 lne
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Day 1 - HW
pg. 216 #’s 1 – 52 (3’s)
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Bacteria in a bottle…There is a single bacterium in a bottle at 11:00pm,
and it is a type that doubles once every minute. The bottle will be completely full of bacteria at 12:00 midnight – exactly one hour.
In your opinion, what percentage of the bottle will be full when the bottle starts to look full? For what amount of time between 11:00 and 12:00 would they have plenty of room to grow and spread out? If you were a researcher in the lab, at what time between 11:00 and midnight might make you look in the bottle and think “I’d better get a bigger container for those bacteria!”?
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Finding Domain of Ln Functions…
f(x)=ln(x-2) *think about the properties of ln
g(x)=ln(2-x)
h(x)=lnx2
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Lets do the application (ex 10) on page 215 together…Graph #41 on page 216
Practice Problems to work on now
pg. 216 #’s 20, 24, 26, 43, 47, 57, 59, 60, 61