 # MATH 242 EXAM 3 STUDY GUIDE

DEFINITIONS AND VOCABULARY:

Inverse function (p94)
One-to-one function (p96)
Horizontal line test (p96)
Transcendental function (p218)
Exponential function (p218)
Natural exponential base e (p222)
Logarithmic function (p229)
Common logarithm (p230)
Natural logarithm (p233)
Properties of logarithms (p230, 240)
Geometric sequence, common ratio (p663, notes)

FORMULAS:

Compound interest formulas (p224): Change of base formula (p239): Exponential growth/decay model (p257, notes): Geometric sequence recursive (p664): Geometric sequence nth term (p664): YOU SHOULD BE ABLE TO:

Find the equation of the inverse of a function given its equation
Graph the inverse of a function given its graph
Show that two functions are inverse functions using composition
Determine whether a function is one-to-one using the horizontal line test
Describe the relationships between a function and its inverse function
Sketch (by hand) and describe the graph of an exponential or logarithmic function , including intercepts ,

asymptotes, domain and range, increasing or decreasing
Use transformations to graph exponential and logarithmic functions
Evaluate exponential or logarithmic functions by hand and using the calculator
Find the equation of an exponential or logarithmic function given its graph
Explain the inverse relationship between exponential and logarithmic functions
Find the domain of a logarithmic function
Change between logarithmic form and exponential form
Use the change of base formula to evaluate or graph a logarithmic function whose base is not 10 or e
Apply the properties of logarithms in simplifying expressions or solving equations
Solve exponential and logarithmic equations algebraically and graphically using your calculator
Solve applied problems involving exponential or logarithmic functions
Find the doubling time or half-life of an exponential growth/decay function
Solve applied problems involving exponential growth/decay or other given models
Recognize a geometric sequence and find the common ratio
Find the terms of a geometric sequence
Find a recursive definition for a geometric sequence
Find the nth term formula for a geometric sequence
Graph a geometric sequence

REVIEW PROBLEMS:

Review Exercises (p117): 139-150; (p271): 1-95, 97-136, 143-150; (p716): 49-60
Chapter Test (p123): 20-22; (p275): 1-29; (p719): 5

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