Question

the domain and range of y=1/(x-2)

Answer 1

Let's start with the domain. There is an x value at which y is undefined: x = 2. y is defined for all other values of x. So, the domain is (-infinity, 2) U (2, infinity)

For the range, think about the graph of the parent function 1/x. It approaches 0 as x goes to infinity, and approaches infinity as x goes to 0.

y=1/(x-2) behaves similarly, as no y shifts exists. The only value it cannot equal is 0, as it approaches 0 but does not reach it.

So, the range is (-infinity, 0) U (0, infinity)