Inverses
Which test do you use to determine if a function is one-to-one?
The horizontal line test
An exponential function can either be a growth or a decay function. If f(x)=bx, then what are the restrictions on b that make it be a growth function? (i.e. what numbers does b take on to grow large?)
b>1
Logarithms and Exponential Functions are _________ of each other
Inverses
What formula do you use when calculating simple interest?
I = Prt
If logarithms are being subtracted, we can combine them and __________ their arguments. In other words,
log (a) - log(b) = log (?)
Divide
= log (a/b)
Determine the inverse of:
y=x3+4
Cuberoot(x-4)
An exponential function can either be a growth or a decay function. If f(x)=bx, then what are the restrictions on b that make it a decay function? (i.e. what numbers does b take on to decrease?)
0<b<1
Let f(x)=log x, what is the domain of this function? What does that make the line x=0?
(0, inf)
Vertical Asymptote
If you were compounding continuously, what formula would you utilize?
A = Pert
If we are adding logarithms, we _________ their arguments to condense into a singular logarithm.
multiply
Determine if the two functions are inverses:
y=(x+6)/2 and y=2(x-6)
No
For a function f(x)=bx, what is the domain of the function always going to be?
(-inf,inf)
What is the range of the function f(x)= log (x-4)
(-inf, inf)
If you were compounding periodically, what formula would you use? What is n?
A = (1+r/n)nt
n is compounding periods per year
Solve 4 log3(2t-7) =8
t=8
To confirm two functions are inverses of each other, what do you have to do?
Composition of functions
f-1(f(x))=x and f(f-1(x))=x
For a function f(x)=bx, what is the range? What does that tell us about y=0?
(0,inf) and that y is a horizontal asymptote
Evaluate ln e13 by hand
Name a type of problem that uses exponential modeling?
Interest, Population Growth, Radioactive Decay, Bacteria, etc.
Solve ln (x2+5x) = ln (-7x-20)
x=-10,-2
If a function is not one-to-one, can a function have an inverse?
No
When two exponential functions are set equal to each other and have the same base, what do we do with the exponents to solve for x?
We set the exponents equal to each other
Simplify the logarithmic expression:
3 log4(a) - 4 log4(b) + 2 log4(c)
3/2 log4(ac/b)
What does loga(1) of any base a equal?
0
If a couple has $80,000 in a retirement
account, how long will it take the money to
grow to $1,000,000 if it grows by 6%
compounded continuously? Round to the
nearest year.
Approximately 42 years