# 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....

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.

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### 1 Answer

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)`