Graphing transformations of exponential functions
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Examples
Lessons
- Horizontal Translation of an Exponential Function
Sketch and compare the graphs of the exponential function y=2x 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=2x and
i) y=2x+1
ii) y=2x−2
Did the transformation affect the horizontal asymptote? - Expansion/Compression of an Exponential Function
Sketch and compare the graphs of the exponential function y=2x and
i) y=23x and y=221x
ii) y=3⋅2x and y=21⋅2x
- Reflection of an Exponential Function
Sketch and compare the graphs of the exponential function y=2x and
i) y=2−x
ii) y=−2x
- Multiple Transformation
Compare to y=2x,
i) Describe the transformations involved in y=6⋅2(x+1)−3.
ii) Sketch both exponential functions on the same graph.
iii) For y=6⋅2(x+1)−3, state its
- asymptote
- domain
- range
- x-intercept
- y-intercept
- Compare to y=2x,
i) Describe the transformations involved in y=−3⋅2(x−2)+6.
ii) Sketch both exponential functions on the same graph.
iii) For y=−3⋅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⋅cb(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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