Nothing Special   »   [go: up one dir, main page]
Scribd Logo
Upload

Welcome to Scribd!

  • 9 views

    Tansformation of Function

    Uploaded by

    stemtvtsmain
    The document discusses various transformations of functions including vertical and horizontal shifting, reflecting, stretching and shrinking. Vertical shifting adds or subtracts a constant to the function, shifting the graph up or down. Horizontal shifting adds or subtracts an input value, shifting the graph left or right. Reflecting reflects the graph across an axis. Stretching and shrinking multiplies the function by a constant greater or less than 1, expanding or compressing the graph vertically or horizontally. These transformations are demonstrated through examples of shifting, reflecting and stretching common functions like parabolas, sine and cosine curves.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Tansformation of Function

    Uploaded by

    stemtvtsmain
    9 views7 pages
    The document discusses various transformations of functions including vertical and horizontal shifting, reflecting, stretching and shrinking. Vertical shifting adds or subtracts a constant to the function, shifting the graph up or down. Horizontal shifting adds or subtracts an input value, shifting the graph left or right. Reflecting reflects the graph across an axis. Stretching and shrinking multiplies the function by a constant greater or less than 1, expanding or compressing the graph vertically or horizontally. These transformations are demonstrated through examples of shifting, reflecting and stretching common functions like parabolas, sine and cosine curves.

    Original Description:

    Original Title

    8.-Tansformation-of-Function

    Copyright

    © © All Rights Reserved

    Available Formats

    PDF, TXT or read online from Scribd

    Did you find this document useful?

    Is this content inappropriate?

    The document discusses various transformations of functions including vertical and horizontal shifting, reflecting, stretching and shrinking. Vertical shifting adds or subtracts a constant to the function, shifting the graph up or down. Horizontal shifting adds or subtracts an input value, shifting the graph left or right. Reflecting reflects the graph across an axis. Stretching and shrinking multiplies the function by a constant greater or less than 1, expanding or compressing the graph vertically or horizontally. These transformations are demonstrated through examples of shifting, reflecting and stretching common functions like parabolas, sine and cosine curves.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    9 views7 pages

    Tansformation of Function

    Uploaded by

    stemtvtsmain
    The document discusses various transformations of functions including vertical and horizontal shifting, reflecting, stretching and shrinking. Vertical shifting adds or subtracts a constant to the function, shifting the graph up or down. Horizontal shifting adds or subtracts an input value, shifting the graph left or right. Reflecting reflects the graph across an axis. Stretching and shrinking multiplies the function by a constant greater or less than 1, expanding or compressing the graph vertically or horizontally. These transformations are demonstrated through examples of shifting, reflecting and stretching common functions like parabolas, sine and cosine curves.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 7

    Tansformation of Function

    (Stewarts Algebra and Trigonometry)

    Vertical Shifting

    Adding a constant to function shifts its graph vertically upward if the constant is
    positive and downward if its negative

    Hence: y = f(x) + c is c units above the y-coordinate of the corresponding point on


    the graph of y = f(x). Similarly, we obtain the graph of y = f(x) − c by shifting the
    graph of y = f(x) downward by c units

    Example
    f(x) = x2 + 1
    f(x) = x2

    f(x) = x2 − 2

    Horizontal shift of the graph

    The graph of y = f(x + c) is the graph of y = f(x) shifted to the left c units
    The graph of y = f(x − c) is the graph of y = f(x) shifted to the right c units

    Example
    1. Graph f(x) = (x − 4)2 and f(x) = (x + 1)2

    f(x) = (x + 1)2 f(x) = x2 f(x) = (x − 4)2


    Combining horizontal and vertical shift
    f(x) = (x − 1)2 + 3

    Graph f(x) = (x − 1)2 + 3


    f(x) = (x − 1)2
    f(x) = x2

    Reflecting graph

    To graph y =− f(x) reflect the graph of y = f(x) in the x-axis


    To graph y = f( − x) reflect the graph of y = f(x) in the y-axis

    y = f(x)
    y = f(x)

    y = f( − x)

    y =− f(x)

    Example
    Graph f(x) =− x2 f(x) = x2

    f(x) =− x2
    Vertical Stretching and Shrinking
    To graph y = cf(x)

    If c > 1 stretch the graph of y = f(x) vertically by a factor of C


    If c <1, shrink the graph of y = f(x) vertically by a factor of C

    y = cf(x) y = f(x)
    y = f(x)
    y = cf(x)

    Example g(x) = 3x2


    f(x) = x2
    1 2
    h(x) = x
    3

    1
    Graph the function y = 3 − 2 (x − 1)2
    y = x2 y = (x − 1)2

    1
    y = 3 − (x − 1)2
    2

    1
    y =− (x − 1)2
    2
    Horizontal shrinking and stretching of Graphs

    1
    If c > 1, shrink the graph of y = f(x) horizontally by a factor of �
    1
    If 0 < c < 1, sketch the graph of y = f(x) horizontally by a factor of �

    y = f(cx)
    y = f(x)

    c>1

    y = f(x)
    y = f(cx)

    0<c<1

    y = f(x)
    y = f(2x)

    1
    y = f( x)
    2

    Transformation of trigonometric function

    f(x) = 1 + cosx
    f(x) =− sinx
    1
    g(x) = sinx
    2
    f(x) = cos2x

    f(x) = cosx + 1

    π 2π 3π 4π

    f(x) = cos2x f(x) = cosx


    f(x) = sinx
    1
    f(x) = sin x
    2
    π 2π 3π 4π

    f(x) =− sinx

    Hence with sine and cosine curve


    y = asink(x − b)
    y = acosk(x − b)
    Amplitude=|a|
    2π
    Period= k
    And phase shift of b

    Graph of Transformation of tangent and cotangent

     Graph the function 4tanx, − tanx

    � � 3� π
    4 2 4

    π
    Graph the function y = tan2x and y = tan2(x − 3 )

    � � 3� π
    4 2 4

    You might also like