| Definitions | Logarithm Jamboree | Exponential Functions | One-to-One Functions | Hodge Podge |
|---|---|---|---|---|
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What is a relation
A set of ordered pairs.
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What is (-inf, inf)
The range of logarithms stays constant and is represented by these values
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Exponential change
Change that is proportional to the starting amount
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domain (0,inf)
range (-inf, inf)
The domain of a function is (-inf, inf) and the range is (0,inf). What will be the inverse's domain and range?
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growth b>1
decay 0
Indicates exponential growth/decay
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What is a function
A relation where there are no repeating inputs.
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No as the inverse of exponential functions, having a base of 0 for a log function will cause the function to be undefined. Think about what happens if an exponential function has a base of 0.
Can we take the logarithm of a negative number? Why or why not?
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a = 1
b = 16
Find the initial value (a) and growth factor (b) of the following:
4^2t |
many answers (x^2, sine)
the domain must be restricted
Give an example of a function that does not have an inverse. What must be done to that function to have an inverse?
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shifting right or left
indicated by log(x +/- c)
For logarithmic functions, these transformations affect the domain.
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What is a one-to-one function
A relation where there are no repeating inputs or outputs.
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What is y=-3
Evaluate without a calculator:
log3(1/27) = y b = 3 |
100e^(-0.173)(3)
(or ~59.5115)
Radon-222 decays at a continuous rate of 17.3% per day. How much will 100 mg of Radon-222 decay to in 3 days?
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No, possible to repeat last name and/or favorite color and invertible functions must be one-to-one
Is the following an example of an invertible function?
Student last name and favorite color |
ln(7xy)
Condense into a single equation:
ln(7)+ln(x)+ln(y) |
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What is an exponential function
f(x) = ab^x, where is a does not equal zero and b is a positive, real number that does not equal 1.
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What is 0, since anything raised to the zero power is 1.
Evaluate without a calculator:
log(1) |
f(x)=2000(0.1)^x
A function that passes through the points (0,2000) and (2, 220).
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graph points and to see if lines are reflected over y=x
find domain and range of functions plug in numbers to see if input and outputs are undone
Give an example of a non-algebraic method of how to determine a function's inverse.
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Domain (2,inf)
Range (-inf, inf) Asymptote x=2 inverse 10^y = 4x-8
Find the domain, range, asymptotes, and inverse of log(4x-8)
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What is a logarithmic function
The power to which we raise b to get x, and the inverse of b^x
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Domain (-inf, 5/4); Range (-inf,inf); asymptote x=5/4); inverse: 10^y = (5-4x)
Find the domain, range, asymptotes, and the inverse of the following:
log(5-4x) |
(1500)(1+(0.03/12))^12*4
You deposit $1500 into a bank account with an annual interest rate of 3% that compounds monthly. Find the balance of the account after 4 years. Leave unsimplified.
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[-7,inf) ; f-1(x)= sqrt(x) - 7
Find the domain where f is one-to-one and not decreasing. Then find the inverse of f restricted to that domain:
f(x) = (x-7)^2 |
x=5
Solve for x:
2^2x+5 = 8^x |
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