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E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals 2.4 E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals The Graph of a Functions KFUPM - Prep Year Math Program (c) All Right Reserved  Domain of a Function  Vertical Line Test  Piecewise Function

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Graphing a function KFUPM - Prep Year Math Program (c) 2009 All Right Reserved

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 1 Specify the domains and ranges of the functions whose graph appears in the following figures:

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 1 Solution GraphFunctionDomainRange

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 2

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 3 must satisfy must satisf

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Vertical Line Test KFUPM - Prep Year Math Program (c) 2009 All Right Reserved It is important to understand that not every graph represents a function. For example, in the given graph the vertical, line L Vertical Line Test meets the graph twice. This means that there are two y-values for the same x where the line L meets the x-axis. Therefore, does not represent a function.

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 4 Determine which of graphs represent the graph of a function. While, the graphs in figures (b), (d), (e) and (f) do belong to functions. Using the vertical line test, we see that the graphs in figures (a) and (c) are not graphs for functions.

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Graph of Basic Functions KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Below are graphs for six basic functions together with some important information about the functions.

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Graph of Basic Functions… cont…. KFUPM - Prep Year Math Program (c) 2009 All Right Reserved

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Graph of Basic Functions… cont…. KFUPM - Prep Year Math Program (c) 2009 All Right Reserved

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Piecewise Functions KFUPM - Prep Year Math Program (c) 2009 All Right Reserved

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 6

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 7

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Increasing, Decreasing and Constant Functions KFUPM - Prep Year Math Program (c) 2009 All Right Reserved

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Turning Points of a Graph KFUPM - Prep Year Math Program (c) 2009 All Right Reserved

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 8