GrAssign - Piecewise Fn Analysis

(G) GrAssign - Piecewise Functions Analysis

   Part I

      ~  Using the algebraic process (as explained in lesson 4.3C) , determine if problems 1 and 2 (right) are continuous.

      ~  For the following problems (1 and 2), assume you are looking for the limit

               1.  as x approaches 2

           2.  as x approaches 0

    A.  If the piecewise function is not continuous, identify the type of discontinuity (jump, hole, infinity). Again, this should be done algebraically.

    ~  Remember, when proving a function is continuous, you must use the definition of continuity, including limits.

     ~   Record your work on the provided document:  Resources: GrAssign - Piecewise Analysis

     ~   You can use Notability to record your work on the above doc.     ~  Show all work.  

NOTE: For Problem #3, change x < 2 to x < -2

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 Part II

   Using Desmos, graph each piecewise function (problems (1 - 4)).

        a.    Using the correct syntax, separately graph each equation of the piecewise function. Syntax:   y = {condition: value}

        b.   Highlight each equation using different graph colors.      

        c.    Add a closed circle if the endpoint(s) is/are included.  

                 If the endpoint(s) is/are not included, identify with an open circle. (See instructions 4.3)      Label and record these points in Desmos notes.

Record your responses to the following questions on the same answer sheet used for Part I. (Right--->

    d.    Looking at the graph, determine if the piecewise equation is a function. Explain why it is or is not a function. Where does it fail to be a function?

    e.    Visually, determine if the function is continuous or discontinuous. (Don't do this algebraically). If discontinuous, identify the type of discontinuity.

    f.    Using interval notation, identify where the function is increasing, decreasing, or constant. The domain is (-∞, ∞).

    ~    Include your name on all graphs.

    ~    Save the graph of each piecewise function separately.

              Gr_Piece_Pr#_LastName      (Change # to 1, 2, 3, or 4)

    ~    Save your answer sheet as GrPiece_Ans_LastName

    ~    Upload your graphs and answer sheet to Google Classroom.

    ~    Point value: 25 pts.

    ~    Include the following as a Desmos Note on your first graph:

    " I pledge my honor, that I will not violate Nazareth's Honor Code during this assignment."