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Chapter 41.9
Graphing transformations of exponential functions
What You'll Learn
Apply horizontal translations by adding or subtracting constants inside exponential functions
Apply vertical translations by adding or subtracting constants outside exponential functions
Recognize how vertical stretches and compressions affect exponential graph steepness
Identify horizontal stretches and compressions by analyzing coefficients of the exponent
Reflect exponential functions across the x-axis and y-axis using negative signs
Determine horizontal asymptotes by analyzing vertical translations
What You'll Practice
1
Graphing exponential functions with horizontal and vertical shifts
2
Sketching graphs with vertical and horizontal stretches or compressions
3
Drawing reflections of exponential functions in both axes
4
Finding asymptotes, domain, range, and intercepts from transformed equations
Why This Matters
Transformations of exponential functions are essential for modeling real-world growth and decay in fields like finance, biology, and physics. Mastering these skills prepares you for advanced calculus topics and helps you interpret how parameters affect exponential models in practical applications.
This Unit Includes
6 Video lessons
Practice exercises
Skills
Exponential Functions
Transformations
Horizontal Translation
Vertical Translation
Reflection
Stretching and Compression
Asymptotes
Graphing
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