What is the Correct General Expression for an Exponential Function?

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SUMMARY

The correct general expression for an exponential function is debated between two forms: y = abc(x+d)+e and y = abcx+d+e. The first expression is preferred for its clarity in demonstrating horizontal shifts, akin to the structure of sine functions. Participants in the discussion agree that while both forms are valid, the first provides a clearer understanding of transformations. This insight is particularly useful for modeling exercises involving exponential functions.

PREREQUISITES
  • Understanding of exponential functions and their properties
  • Familiarity with mathematical modeling techniques
  • Knowledge of function transformations, including horizontal shifts
  • Basic grasp of sine functions for comparative analysis
NEXT STEPS
  • Research the properties of exponential functions in detail
  • Study function transformations, focusing on horizontal and vertical shifts
  • Explore mathematical modeling techniques using exponential functions
  • Learn about the relationship between exponential and trigonometric functions
USEFUL FOR

Mathematicians, educators, students in advanced mathematics, and anyone involved in modeling exercises that utilize exponential functions.

Peter G.
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Hi,

I am working on a modeling exercise and I would like to know which is the correct general expression for a Exponential Function:

y = abc(x+d)+e

or

y = abcx+d+e

Thanks in advance,
Peter G.
 
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Peter G. said:
Hi,

I am working on a modeling exercise and I would like to know which is the correct general expression for a Exponential Function:

y = abc(x+d)+e

or

y = abcx+d+e

Thanks in advance,
Peter G.

Either would be fine, IMO, although the first makes horizontal shifts more obvious.
 
Hi,

Thanks a lot for your response! I also prefer the first one because it reminds me of how the Sine Function is set up, making, as you said, the horizontal shift more obvious for me.
 

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