Transforming Piecewise Functions

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Homework Help Overview

The discussion revolves around transforming a piecewise function through a series of specified transformations, including reflection, horizontal stretch, translation, and vertical stretch. The original function consists of three segments defined over different intervals of x.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss how the transformations affect the function's domain and the implications of reflecting the borders of the piecewise function. There is an exploration of the effects of reflecting the border at x = -1 and whether it remains unchanged.

Discussion Status

The discussion is ongoing, with participants questioning the effects of transformations on the function's borders and domain. Some guidance has been offered regarding the reflection of the border, but multiple interpretations are still being explored.

Contextual Notes

There is uncertainty regarding how the transformations specifically alter the domain of the piecewise function, and participants are considering the implications of each transformation on the defined intervals.

Mjucewitz

Homework Statement


The piece wise function is
-x-2, x<-1
x^2-3x, -1≤ x ≤5
3x+5, x>5
The problem is to transform the function with these series of transformations
  • reflection in the x-axis
  • Horizontal stretch by a factor of 6
  • Translation left 3 units
  • Vertical Stretch by a factor of 4

Homework Equations


The basic transformation rules for a function

The Attempt at a Solution


I was able to transform the function part, but I can not figure out how the domain is suppose to be affected by the transformations. All I have is
((2x)/3) + 20
(((-2x^2)/3)+12) + (2x+3)
-2x-8
Update: I tried my best at the domain and got:
x<12
12≤x≤48
x>48
 
Last edited by a moderator:
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One of the borders is x=-1. What happens if you reflect this border at the x-axis, or do one of the other operations?
 
mfb said:
One of the borders is x=-1. What happens if you reflect this border at the x-axis, or do one of the other operations?
If you were to reflect the border x = -1 over the x-axis would it not stay the same?
 
Right.
What happens with the other operations?
 

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