Graphing transformations of exponential functions

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Examples
Lessons
  1. Horizontal Translation of an Exponential Function
    Sketch and compare the graphs of the exponential function y=2xy=2^x and
    i)
    y=2(x+1)y=2^{(x+1)}
    ii)
    y=2(x2)y=2^{(x-2)}

    Did the transformation affect the horizontal asymptote?
    1. Vertical Translation of an Exponential Function
      Sketch and compare the graphs of the exponential function y=2xy=2^x and
      i)
      y=2x+1y=2^x+1
      ii)
      y=2x2y=2^x-2

      Did the transformation affect the horizontal asymptote?
      1. Expansion/Compression of an Exponential Function
        Sketch and compare the graphs of the exponential function y=2xy=2^x and
        i)
        y=23xy=2^{3x} and y=212xy=2^{\frac{1}{2}x}
        ii)
        y=32xy=3 \cdot 2^x and y=122xy=\frac{1}{2} \cdot 2^x

        1. Reflection of an Exponential Function
          Sketch and compare the graphs of the exponential function y=2xy=2^x and
          i)
          y=2xy=2^{-x}
          ii)
          y=2xy=-2^x

          1. Multiple Transformation
            Compare to y=2xy=2^x,
            i)
            Describe the transformations involved in y=62(x+1)3y=6 \cdot 2^{(x+1)}-3.
            ii)
            Sketch both exponential functions on the same graph.
            iii)
            For y=62(x+1)3y=6 \cdot 2^{(x+1)}-3, state its
            - asymptote
            - domain
            - range
            - x-intercept
            - y-intercept
            1. Compare to y=2xy=2^x,
              i)
              Describe the transformations involved in y=32(x2)+6y=-3 \cdot 2^{(x-2)}+6.
              ii)
              Sketch both exponential functions on the same graph.
              iii)
              For y=32(x2)+6y=-3 \cdot 2^{(x-2)}+6, state its
              - asymptote
              - domain
              - range
              - x-intercept
              - y-intercept
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              Topic Notes
              Do you know how to sketch and state transformations of exponential functions graphs? How about applying transformations to exponential functions including, horizontal shift, vertical shift, horizontal expansion/compression, vertical expansion/compression, reflection and inverse? You will learn them all in this lesson!
              y=acb(xh)+ky=a \cdot c^{b(x-h)}+k
              a=a = vertical expansion/compression
              b=b = horizontal expansion /compression
              h=h = horizontal translation
              k=k = vertical translation
              • Reflection?