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3: Graphs

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Learning Objectives

    • Interpret, from function notation, an action or several actions to be taken on a known function, \(f\), in order to sketch the transformed function.
    • Sketch transformations from \(9\) familiar functions.
    • Write the equation of a function associated with descriptive transformations such as shifting left, right, up, or down, reflecting, stretching, and compressing of its parent function.

    • 3.1: Transformations of f(x)
      In this section, you will practice manipulating a given graph, according to the corresponding function notation. We’ll use the function f for demonstration throughout this section. But any graph will do!
    • 3.2: Transformations of Common Graphs
      The transformation of graphs, using common functions, will be a skill that will bring insight to graphing functions quickly and painlessly. Anticipating how a graph of a function will look, and transforming old graphs to new graphs, is a skill we will explore in this section. Mastering this skill will give you a leg up on understanding analytic geometry, a key component to calculus.

    This page titled 3: Graphs is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Jennifer Freidenreich.

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