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Transforming Piecewise Functions

  1. Oct 29, 2017 #1
    1. The problem statement, all variables and given/known data
    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

    2. Relevant equations
    The basic transformation rules for a function

    3. 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: Oct 29, 2017
  2. jcsd
  3. Oct 29, 2017 #2

    mfb

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    2016 Award

    Staff: Mentor

    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?
     
  4. Oct 29, 2017 #3
    If you were to reflect the border x = -1 over the x axis would it not stay the same?
     
  5. Oct 29, 2017 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Right.
    What happens with the other operations?
     
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