Transforming Functions: From f(x+1) to f(x)

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Discussion Overview

The discussion revolves around transforming the function f(x+1) = x into a function expressed solely in terms of x, specifically f(x). Participants explore the implications of this transformation, the graphical representation of the functions involved, and the relationships between the variables.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that by letting y = x + 1, one can derive f(y) = y - 1, leading to f(x) = x - 1.
  • Others argue that f(x + a) represents a shift of f(x) on the x-axis, specifically to the left by a.
  • A participant questions whether substituting x in the transformation affects the relationship between the variable and the function, potentially leading to incorrect results.
  • Some participants clarify that f(x + 1) = x is not graphically the same as f(x) = x, as they represent parallel lines with different intercepts.
  • There is a discussion about the derivative of the functions, noting that while the derivatives may be the same, the graphs are distinct and consistently offset by one unit.
  • A participant expresses confusion regarding the equivalence of the graphs and the implications of the transformations discussed.

Areas of Agreement / Disagreement

Participants generally do not reach consensus on the implications of the transformations and their graphical representations, with multiple competing views remaining regarding the relationships between the functions and their graphs.

Contextual Notes

There are unresolved questions about the implications of substituting variables in the context of specific problems, as well as the graphical interpretations of the functions involved.

  • #31
BloodyFrozen said:
Sorry, but I haven't quite understood what you have said. Perhaps you could clarify or another person could answer. :)

Hi

I'm just curious because, f(x+1)=x is f(x)=x-1 shifted one to the left, so their graphs must not look identical right? And so we cannot equate f(x+1)=f(x)?
 
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  • #32
Actually, f(x)=x-1 is shifted one down or one to the right (from f(x)=x).
 
  • #33
BloodyFrozen said:
Actually, f(x)=x-1 is shifted one down or one to the right (from f(x)=x).

Hi

I meant that the graph of f(x+1) = x is the graph of f(x) = x-1 shifted one left.
 
  • #34
Red_CCF said:
Hi

I meant that the graph of f(x+1) = x is the graph of f(x) = x-1 shifted one left.

They're the same thing
 
  • #35
BloodyFrozen said:
They're the same thing

I apologize for dwelling on this, but I'm really confused. I read from Stewart's Calculus that y = f(x+c) shift the graph of y = f(x) c units to the left. If the function is shifted their graphs are different so how can be the same?

Thanks
 

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