You should be able to do the fol lowing :
INVERSE FUNCTION CONCEPT (5.2)
• Know that a function returns one output value for each input value.
• Understand that an inverse function is the "undo" of a function.
• Know that the symbol for inverse of a function f is f -1. It does not mean
reciprocal.
• Given a verbal description for a function f, give a verbal description for
f -1. 
[opposite operation]
• Given a formula for a function f, give a formula for f -1.
["undo" the steps ]
• Given a table for a function f, give a table for f -1.
[swap the input and output columns]
• Given a graph for a function f, give a graph for f -1.
[swap the x and y co-ordinates]
("flip"
around the line y = x)
• Know that the inverse of an exponential function is a logarithmic function.
• Understand that the inverse of a composition of functions is the composition
of the inverse functions, but in reverse order :
EXPONENTIAL FUNCTIONS (R.3, R.7, 5.3, 5.6)
• Know the equivalent meanings of
negative exponents
fraction exponents
any rational- number exponent (in fraction or decimal form)
• Use the three basic properties of exponents .
• Recognize (without a calculator) certain powers of small whole numbers:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144,...
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000,
1, 16, 81, 256, 625, ..., 10000,
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192...
• Calculate rational powers of rational numbers (without a calculator).
• Sketch a rough "cartoon" of an exponential function.
• Understand that an asymptote provides a long- term trend for a graph.
• Know that every exponential function can be written in the form f(x) = Cax.
• Explain, using examples, the difference between linear growth and exponential
growth.
• Describe (in words) the difference between linear and exponential growth.
• Remember that
multiplying by a positive
|
1 |
leaves alone |
|
number larger than 1 |
enlarges |
|
number smaller than 1 |
reduces |
• Know that
a P% increase is the same as multiplying by (1 + 0.01P)
a P% decrease is the same as multiplying by (1 - 0.01P)
• Given an amount, apply a percent increase/decrease.
• Given an amount with a percent increase/decrease, find the original amount.
• Remember that interest rates are assumed to be annual.
• Know what is meant by compounding (annually, quarterly, monthly, daily).
• Given the interest rate, frequency of compounding, length of time, and present
value of an investment, calculate the future value.
• Given the interest rate, frequency of compounding, length of time, and future
value of an investment, calculate the present value.
• Given data, find an exponential function that fits the data.
LOGARITHMIC FUNCTIONS (5.4, 5.5, 5.6)
• Know that logarithms are exponents!
• Given a statement in logarithmic form, write an equivalent statement in
exponential form.
• Given a statement in exponential form, write an equivalent statement in
logarithmic form.
• Sketch a rough "cartoon" of a logarithmic function.
• Know and use the three basic properties of logarithms.
• Use properties of logarithms to solve exponential and logarithmic equations .
• Calculate logarithms of rational numbers (without a calculator).
• Given the interest rate, frequency of compounding, present value, and future
value of an investment, calculate the length of time
required.
• Given the interest rate and frequency of compounding of an investment ,
calculate the doubling time, tripling time, quadrupling
time, etc.
• Solve other application problems involving exponential growth or decay,
particularly ones related to Newton’s law of cooling
(or heating) and population growth or decay.
