{"id":29090,"date":"2021-08-19T13:00:35","date_gmt":"2021-08-19T13:00:35","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29090"},"modified":"2024-09-22T09:28:14","modified_gmt":"2024-09-22T09:28:14","slug":"domain-range-and-graph-proposed-and-solved","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/en\/domain-range-and-graph-proposed-and-solved\/","title":{"rendered":"Domain, Range, and Graph – Proposed and Solved"},"content":{"rendered":"

<\/p>\n

Domain, Range, and Graph – Proposed and Solved<\/h1>\n

Summary:<\/strong>
\n In this class, we practice how to determine the domain, range, and graph of algebraic functions through exercises and solved examples, highlighting the importance of practice to master these techniques.
\n <\/em><\/p>\n

Learning Objectives:<\/strong>
\n By the end of this class, the student will be able to:<\/p>\n

    \n
  1. Understand<\/strong> how to determine the domain of algebraic functions.<\/li>\n
  2. Identify<\/strong> the range of different types of functions.<\/li>\n
  3. Represent<\/strong> the graph of algebraic functions in the Cartesian plane.<\/li>\n
  4. Apply<\/strong> simplification techniques to solve more complex functions.<\/li>\n<\/ol>\n

    <\/center><\/p>\n

    How to Master the Techniques<\/h2>\n

    To master the techniques that allow you to determine the domain, range, and graph, at least at this level, it is not necessary to review more theory than we have already covered. At this point, it is better to do exercises, and the best way to practice is by randomly inventing exercises. Only in this way will you truly know the limits of the techniques we have studied so far and develop the intuition that will allow you to perform with skill.<\/p>\n

    What we will do next is exactly that: I will invent some random exercises and solve them as the techniques reviewed permit; if they cannot be solved with them, I will explain at which points they fail and why.<\/p>\n

    Practice Exercises:<\/h3>\n

    Determine the domain, range, and graph of the following functions:<\/p>\n

      \n
    1. a(x) = \\displaystyle \\frac{x^3 - 3x^2 + 5x - 1}{x^2 + 2x - 1}<\/span><\/li>\n
    2. b(x) = \\displaystyle \\frac{4x^4 + 2x^3 - 5x^2 - 2x - 2}{2x^2 - x - 1}<\/span><\/li>\n
    3. c(x) = \\displaystyle \\frac{x^5 + x^3 - x - 1}{x^2 - x - 1}<\/span><\/li>\n
    4. d(x) = \\displaystyle \\frac{3x^2 - 3x - 2}{\\sqrt{x^2 - 1}}<\/span><\/li>\n
    5. e(x) = \\displaystyle \\sqrt{\\frac{x^4 - x^2 - 11}{(x^2 - 1)\\sqrt{x^2 - x - 1}}}<\/span><\/li>\n
    6. f(x) = \\displaystyle \\frac{(x^2 - 2x - 2)\\sqrt{7x^8 - 5x^4 - 2}}{x\\sqrt{5x^2 - 3x + 2}}<\/span><\/li>\n<\/ol>\n

      Practice Exercises Solution:<\/h3>\n