Graphing transformations of exponential functions

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Now Playing:Graph transformation of exponential functions– Example 1

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

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

Did the transformation affect the horizontal asymptote?
Expansion/Compression of an Exponential Function
Sketch and compare the graphs of the exponential function $y=2^x$ and
i)
$y=2^{3x}$ and $y=2^{\frac{1}{2}x}$
ii)
$y=3 \cdot 2^x$ and $y=\frac{1}{2} \cdot 2^x$
Reflection of an Exponential Function
Sketch and compare the graphs of the exponential function $y=2^x$ and
i)
$y=2^{-x}$
ii)
$y=-2^x$
Multiple Transformation
Compare to $y=2^x$ ,
i)
Describe the transformations involved in $y=6 \cdot 2^{(x+1)}-3$ .
ii)
Sketch both exponential functions on the same graph.
iii)
For $y=6 \cdot 2^{(x+1)}-3$ , state its

- asymptote
- domain
- range
- x-intercept
- y-intercept
Compare to $y=2^x$ ,
i)
Describe the transformations involved in $y=-3 \cdot 2^{(x-2)}+6$ .
ii)
Sketch both exponential functions on the same graph.
iii)
For $y=-3 \cdot 2^{(x-2)}+6$ , state its

- asymptote
- domain
- range
- x-intercept
- y-intercept

y=a \cdot c^{b(x-h)}+k

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