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
What is the new domain and range? Can you please tell me how to solve this without graphing.
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
Domain: `(-oo,0) uu (0,oo)`
all real #'s excluding zero
Range: `(-7, 3) uu (-oo, -7)`