Writing the equation of a transformed exp function given the graph

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SUMMARY

The discussion focuses on transforming the exponential function f(x) = 2^x based on a specific graph, referred to as graph B. Participants emphasize the importance of identifying the transformation parameters, including a, b, k, and d, while noting that the asymptote is set at c = 0. The consensus is that a systematic approach using two known points on the graph can help establish a system of equations to derive the equation of the transformed function.

PREREQUISITES
  • Understanding of exponential functions and their transformations
  • Familiarity with the general form of exponential equations, specifically ab^x
  • Knowledge of systems of equations and how to solve them
  • Basic concepts of asymptotes in graphing functions
NEXT STEPS
  • Research how to derive transformation parameters for exponential functions
  • Learn about graphing techniques for identifying transformations
  • Study systems of equations in the context of multiple variables
  • Explore the implications of asymptotes on the behavior of exponential functions
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Students studying algebra, mathematics educators, and anyone interested in understanding transformations of exponential functions.

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Homework Statement



EXPONENTIAL FUNCTION

The graph represents a transformation of the function f(x) = 2^x, Write an equation for it.

The graph in question is the second one, graph B.

http://ars.els-cdn.com/content/image/1-s2.0-S0006349598778683-gr1.gif

Since there are more variables involved I am not sure how to solve. I know if its just ab^x then I can find two points and do a system of equations. But what is the process when I have, k, a, d variables to worry about as well. I know that c is 0 because its the asymptote. Can someone please help. Thanks!
 
Last edited:
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There's no way to solve this as a completely open-ended question. You have to make some assumption about the general form of the transformation. Suggest something.
 

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