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Graphing Transformations of Exponential Functions
See exactly how shifts, reflections, and stretches move and reshape an exponential graph, with clear rules and worked examples.
What You'll Learn
Every transformation of an exponential function comes from changes to the general form y equals a times b to the power of x minus h, plus k
The value of k shifts the graph and its horizontal asymptote up or down, while h shifts the graph left or right
A negative sign in front of a (or on the exponent) reflects the graph across the x axis or the y axis
The size of a stretches or compresses the graph vertically, but it never changes the horizontal asymptote
Combining several transformations at once just means applying each rule to the parent graph one at a time
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
Learning resources
Skills
Exponential Functions
Transformations
Horizontal Translation
Vertical Translation
Reflection
Stretching and Compression
Asymptotes
Graphing
ON Curriculum Aligned