What is the domain and range of 1/x?

Domain: All real numbers except 0. Range: All real numbers except 0.

Graph of y = 1/x

The graph of y = 1/x is a rectangular hyperbola with two branches, in the first and third quadrants.

Domain	All real numbers except 0
Range	All real numbers except 0
Symmetry	Odd: symmetric about the origin
Increasing / decreasing	Decreasing on (−∞, 0) and on (0, ∞)
Key feature	Asymptotes x = 0 and y = 0; the graph never touches either axis

(−2, −0.5)
(−1, −1)
(0.5, 2)
(1, 1)
(2, 0.5)

In y = a/(x − h) + k, the asymptotes move to x = h and y = k.

a stretches the graph vertically and flips it when negative. h shifts it right (left when negative). k shifts it up (down when negative).