Transforming Piecewise Functions

  • #1
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:

Answers and Replies

  • #2
34,849
11,017
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?
 
  • #3
Mjucewitz
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?
 
  • #4
34,849
11,017
Right.
What happens with the other operations?
 

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