# Graphing transformations of exponential functions

##### Examples

###### Lessons

**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

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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!

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

• $a =$ vertical expansion/compression

• $b =$ horizontal expansion /compression

• $h =$ horizontal translation

• $k =$ vertical translation

• Reflection?

• $a =$ vertical expansion/compression

• $b =$ horizontal expansion /compression

• $h =$ horizontal translation

• $k =$ vertical translation

• Reflection?

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