Write a reciprocal function translated to the right by 3, has a vertical stretch of 2, and is reflected over the y-axis. Determine the domain and range.

Answer 1

consider f(x) = 1/x
domain: x≠0
range y≠0
translate right 3: 1/(x-3)
stretch: 2/(x-3)
reflect: 2/((-x)-3) = -2/(x+3)
domain: x+3≠0, so x ≠ -3
range: y≠0

see the graphs at
www.wolframalpha.com/input/?i=plot+y%3D1%2Fx%2C+y%3D2%2F%28-3-x%29