Transformations of Exponential Functions
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Subject Area: Mathematics (B.E.S.T.) | Grade Level: 9
Lesson Length: 30 minutes
Keywords/Tags: Exponential Functions, Function Transformations, Transformations
Lesson Description: In this lesson, students will investigate the effects of a, h, and k on the parent function y = b^x. They will be able to describe the transformations and write equations of transformed functions.

  • Other MGSE9-12.F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology
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Video : Transformation of Exponential Functions
Instructions: Please watch the following video as many times as needed before starting to go through other lesson pages. Understanding the content of the video is very important since the lesson activities will be all about this video content.
Description: A tutorial/overview of the effects of a, h, and k on the graph of the function y=b^x.
Resources : Additional Resources
Instructions: Please see additional external resources below. Feel free visit each link to learn more about this lesson.
Transforming Exponential Functions
Find further explanation, along with examples and visuals, of the transformation of exponential functions.
Quizlet - Transformation of Exponential Functions
Use these cards to quiz and refine your understanding of the transformations of y = (b)^x created by a, h and k.
Horizontal and Vertical Shifts
This website focuses on the values of h and k in a transformed exponential function, detailing their effects on domain, range, and asymptote of the function.
Description: Further explanation of the effect a, h, and k have on the parent function y=a(b)^x.
Quiz : Identifying Transformations
Instructions: Please complete this quiz by choosing the correct answer for each question. You can take this quiz as many times needed.
Question #1

What is the parent function of the function y = 2(3)^(x-1)+5?

Question #2

Which transformation has occured to the parent function y = 2(1/2)^(x-1)?

Question #3

Which function below represents a function in which the parent function has been compressed vertically?

Question #4

Does the function y = 0.5(3)^x represent growth or decay?

Question #5
A graph that has been vertically stretched will have points that are closer to the y-axis.
Question #6
Has the function y = -2(3)^x+4 been reflected over the x-axis?
Question #7
Has the function y = -2(3)^x+4 been vertically compressed?
Question #8
The parent function in y = (1/2)^(x-2)+5 been reflected across the x-axis.
Question #9
The parent function in the function y = 3(1/8)^(x-5) has been shifted down 5. 
Question #10
Which value - a, h, or k - effects the asymptote?  Make your choice and explain "how" the value effects the asymptote.
Description: A quick check over the effects of a, h, and k to the parent function y = b^x.
Forum : Talk it out!
Instructions: Students: Please complete an initial response to at least one of the following.
h and k
Discuss how h and k are similar and how they differ in their presence in the equation and effect on the parent function.
Stretch and Shrink
Graphically, compare and contrast a stretch and shrink of parent function such as y=b^x.
Question I have...
What specific questions do you have?
Description: Time to try to articulate your understanding of transformation of exponential functions.