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Rational Functions

Rational Function

Study Guide for Exam #4

Chapter 7.1-8(~7.6) Rational Functions
Chapter 8.1-5 Exponential and Logarithmic Functions

The exam will be based upon your homework, the material we covered in class, along with
the reading as signments . It will be in class on Monday, November 24, and you will have
75 minutes to complete it. This study guide provides an overview of the material we have

Chapter 7.1 Introducing Rational Functions
Understand what a rational function is
Know where rational functions are undefined
Find the domain and range
The graph of

Chapter 7.2 Reducing Rational Functions
Reduce and expression to lowest terms
Understand the restrictions on a function

Chapter 7.3 Graphing Rational Functions
Find the zeros of a rational function
Vertical asymptotes (or holes) occur where the function is undefined!
Sketch a rational function without the calculator

Chapter 7.4 Products and Quotients of Rational Functions

Recall the cancellation rule found on page 644
Remember previous material regarding vertical asymptotes and holes

Chapter 7.5 Sums and Differences of Rational Functions
Know how to find the LCM

Chapter 7.7 Solving Rational Equations
Clear the fractions from a rational equation

Chapter 7.8 Applications of Rational Functions
Write and solve an equation that uses a number and its reciprocal
Be able to solve Distance, Speed and Time problems using the equation d = rt
Be able to solve Work problems using the equation W = rt

Chapter 8.1 Exp onents and Roots
Know and use the laws of exponents
Know the domain and range of the square root function
Know the domain and range of the cube root function
Know the domain and range of even and odd root functions

Chapter 8.2 Exponential Functions
Use the exponential function f (t) = Abt , where A is the initial amount, and b > 0,b ≠ 1
Distinguish between exponential growth (b > 1) and decay (0 < b < 1)
Know the properties of an exponential function

Chapter 8.3 Applications of Exponential Functions
Discrete Compound Interest :

Continuous Compound Interest:

Find the future value of an investment

Chapter 8.4 Inverse Functions
De termine if a function is one-to-one. If so, the function passes the Horizontal Line Test
and has an inverse function.
Find the inverse function (both graphically and algebraically )

Chapter 8.5 Logarithmic Functions
Use one of the following exponential or logarithmic formulas to find the other.

Use the following properties:

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