Graph Transform: x(-n-1) Impact

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SUMMARY

The function transformation represented by x(-n-1) involves two key operations: a reflection across the y-axis and a horizontal shift to the left by one unit. Specifically, the notation y = f(-x - 1) indicates that the graph of the original function f(x) is first reflected and then translated. This is consistent with the established transformations where y = f(x - 1) shifts the graph right and y = f(-x) reflects it across the y-axis. The combination of these transformations results in a graph that is both reflected and shifted.

PREREQUISITES
  • Understanding of function transformations in graphing
  • Familiarity with the notation of function shifts and reflections
  • Knowledge of basic algebraic functions, such as quadratic functions
  • Ability to interpret graphical representations of mathematical functions
NEXT STEPS
  • Study the properties of function transformations in detail
  • Learn about the effects of horizontal and vertical shifts on graphs
  • Explore the concept of reflections in graphing functions
  • Analyze specific examples of quadratic functions and their transformations
USEFUL FOR

Mathematics students, educators, and anyone interested in understanding graph transformations and their implications in algebraic functions.

andrey21
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How would the following function impact on a graph?

x(-n-1)



Heres what I know:

x(n-1) shift graph right by 1 step
x(-n) reflect in y axis


So would the solution be reflect in y-axis and shift right by 1??
 
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Would it be reflected in y-axis and shifted left by 1 step??
 
Your "x(n - 1)" notation is very unusual, especially if you're also talking about y.

If y = f(x), then the graph of y = f(x - 1) is the translation of the graph of f by one unit to the right.

The graph of y = f(-x) is the reflection across the y-axis of the graph of f.

y = f(-x - 1) = f(-(x + 1)) consists of a reflection and a translation, in that order.

Think about how y = (-x - 1)2 looks in comparison to the untransformed function f(x) = x2.
 

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