# A function has a domain of x is the element of all real number such that it doesnot equal to 0. It has a range of y is the element of all real numbers such that -8<y<2 or 2<y<infinity. it goes through the transformation: reflection about the x axis vetical compression by 1/2 horizontal stertch by 3 down 5 What is the new domain and range? Can you please tell me how to solve this without graphing.

## Expert Answers

Since your function does not move left or right, the domain will remain the same as the reflection across the x-axis will still remain all real numbers except zero.  A vertical compression and horizontal stretch will not affect the domain or range.  Since the graph is moving down 5 units this will affect the range of the function.  Everything will shift down 5 units.  Therefore an original range of -8<y<2 or 2<y<infinity will now be -2<y<8 or -infinity<y<-2 reflected across the x-axis.  Shifted 5 down will be -7<y<3 or -infinity < y < -7

Therefore:

Domain:  `(-oo,0) uu (0,oo)`

all real #'s excluding zero

Range:  `(-7, 3) uu (-oo, -7)`

Approved by eNotes Editorial Team

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