# 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 $y=2^x$ and
i)
$y=2^{(x+1)}$
ii)
$y=2^{(x-2)}$

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

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

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

1. 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
1. 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
###### 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!
$y=a \cdot c^{b(x-h)}+k$
$a =$ vertical expansion/compression
$b =$ horizontal expansion /compression
$h =$ horizontal translation
$k =$ vertical translation
• Reflection?