How Does Shifting Affect the Function f(x)?

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SUMMARY

The discussion focuses on the function transformation involving the polynomial f(x+a1) = x^2 + x + 2 and seeks to determine f(x-a). The key insight is that f(anything + a) translates to (anything)^2 + anything + 2, prompting the need to express f(x-a) in a similar form. Participants also explore the implications of the variables a and a1, questioning their roles in the function's behavior and their relationship to absolute value.

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  • Understanding polynomial functions and their transformations
  • Familiarity with function notation and variable manipulation
  • Basic knowledge of absolute value concepts
  • Experience with algebraic expressions and equations
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  • Study polynomial function transformations in detail
  • Learn about the implications of shifting functions in algebra
  • Research the role of absolute value in function behavior
  • Explore the differences between variable representations in mathematical functions
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If

f(x+a1) = x^2 + x + 2



then what is

f(x-a)



Please help!
 
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this seems to mean that f(anything +a) = (anything)^2 + anything + 2.

so here you have to write f(x-a) as f(something + a), and then apply the polynomial above to th something. what would the something be?
 
1. What does this have to do with absolute value?

2. What is the difference between a and a1? What do they mean?
 

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