# Graphing transformations of exponential functions

### Graphing transformations of exponential functions

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!

#### Lessons

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

• 2.
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?

• 3.
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 $y=\frac{1}{2} \cdot 2^x$

• 4.
Reflection of an Exponential Function
Sketch and compare the graphs of the exponential function $y=2^x$ and
i)
$y=2^{-x}$
ii)
$y=-2^x$

• 5.
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

• 6.
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