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1: Relations and Functions

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    119140

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    • 1.1: Sets of Real Numbers and the Cartesian Coordinate Plane
      This section introduces the sets of real numbers, their properties, and the Cartesian coordinate plane. It covers the classification of numbers (natural, whole, integers, rational, and irrational) and explains how to plot points and graph equations on the Cartesian plane. The section also discusses intervals and the distance formula, providing foundational knowledge for working with functions and graphs in Algebra.
    • 1.2: Relations
      This section introduces relations, explaining how they are defined as sets of ordered pairs. It provides examples of different types of relations and discusses how to represent relations graphically and algebraically.
    • 1.3: Introduction to Functions
      This section introduces the concept of functions, distinguishing them from general relations. It explains the definition of a function, including the ideas of domain and range. The section covers the concept of the Vertical Line Test to determine if a relation is a function, and provides examples to illustrate these ideas.
    • 1.4: Function Notation
      This section explains function notation, including how to interpret and evaluate functions expressed in this form. It covers the use of symbols like f(x) to denote functions, how to substitute values into functions, and how to read and write functions in different contexts. Examples are provided to illustrate these concepts, emphasizing the importance of understanding function notation for further study in Algebra.
    • 1.5: Function Arithmetic
      This section focuses on function arithmetic, covering how to perform operations like addition, subtraction, multiplication, and division with functions. It explains how to evaluate these operations for given inputs and discusses the concept of the domain of combined functions. Examples are provided to illustrate these operations and their practical applications, emphasizing understanding of function combinations.
    • 1.6: Graphs of Functions
      It’s time to look at functions graphically again, only this time we’ll do so with the notation defined in Section 1.4.
    • 1.7: Transformations
      This section covers transformations of functions, including translations, reflections, stretches, and compressions. It explains how to apply these transformations to function graphs and how changes in function equations affect their graphs. The section provides examples and visual aids to illustrate vertical and horizontal shifts, reflections over the axes, and scaling of graphs. These concepts help understand how functions can be manipulated to model different real-world scenarios.

    This page titled 1: Relations and Functions is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Carl Stitz & Jeff Zeager via source content that was edited to the style and standards of the LibreTexts platform.