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5: Functions

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    Learning Objectives

    By the end of this chapter, the student should be able to

    • Evaluate and define a function
    • Identify the independent and dependent variable and their units
    • Apply algebraic operations on functions
    • Recognize the shape of a function’s graph with its name and formula

    There are many different types of equations that we can work with in algebra because an equation gives the relationship between a variable(s) and numbers. For example,

    \[\dfrac{(x-3)^2}{9}-\dfrac{(y+2)^2}{4}=1\quad\text{or}\quad y=x^2-2x+7\quad\text{or}\quad\sqrt{y+x}-7=xy\nonumber\]

    all give relationships between variables and numbers. Some of these relationships are called functions.

    Definition: Function

    A function is when one input of a relation is linked to only one output of the relation, i.e., a function has only one \(y\) for one \(x\).

    Function notation is represented by \(f(x)\) such that \[f(x) = y,\nonumber\] and we say \(f\) is a function of \(x\).

    This page titled 5: Functions is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Darlene Diaz (ASCCC Open Educational Resources Initiative) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.