# 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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