Study Guide for Test No.2
Test will be on Friday, February 27, 2009
You need to know the following new material:
Section 2.1(functions and their graphs)
Given a function calculate the domain of the function. See exercises 21 through 33 on page 59 of your
textbook.
Given a function f(x), calculate the function of a given f(a) for some a of the domain of the function. See
exercises 1 through 14 on page 58 of your textbook.
Given a function and a point, determine if the point lies on the graph of the function. See exercises 17 through
20 on page 59 of your textbook.
Given a graph determine if this graph represents y as a function of x. See exercises 49 through 55 on pages 59
and 60 of your textbook. Read the vertical-line test on page 56-57 of your textbook.
Section 2.2 (Algebra of functions)
Given the definitions of two functions f(x) and g(x) find the new functions defined as the sum, difference,
product, and quotient of these functions. Know how to determine the domain of the sum, difference, product,
and quotient of these functions. See Example 1 (on page 69). See also exercises 1 through 24 on pages 73 and
74 of your textbook. For all these functions determine the domain. Remember that for the sum, difference, and
product the domain is the defined as the intersection of the domains of the individual functions. Intersection
means the common elements of the domain of both functions.
2.2 (Composition of functions)
Given two functions f(x) and g(x) find the composition (g◦f)(x) and (f◦g)(x). See example 4 on page 72 of your
textbook. See exercises 25 through 34 on page 74 of your textbook.
Section 2.4 (Limits)
Given the graph of a function, you need to know if the function has a limit for a given value x = a of the domain
of the function. See Example 3 on page 101 of your textbook. See exercises 1 through 8 on page 111 of your
textbook.
Given a function calculate the limit of a given value x =a of the domain of the function. See Example 4 on page
102 and 103 of your textbook. See exercises 23 through 62 on pages 112 and 113 on your textbook. In
particular pay attention to exercises 49 through 62. You may need to consult table 6 on page 14 for some of the
factorizations that you may require to do the exercises of this section. Remember to use the rules of Theorem
No. 1 on page 102 of your textbook.
2.4 (Limits at infinity)
Given a limit at infinity know how to calculate it by using the rule given on page 108 of your textbook. See
Example 8, 9, and 10 on pages 108 and 109 of your textbook. See exercises 73 through 80 on page 114 of your
textbook.
