# What is the domain and range of #f(x) = 1/(x-2) #?

##### 1 Answer

Domain:

Range:

#### Explanation:

Your function is defined for any value of **except** the one that can make the denominator equal to zero.

#x-2 = 0 implies x = 2#

This means that

The range of the function will be affected by the fact that the only way a fraction can be equal to **zero** is if the numerator is equal to zero.

In your case, the numerator is constant, euqal to

#f(x) != 0", "(AA)x in RR-{2}#

The range of the function will thus be

graph{1/(x-2) [-10, 10, -5, 5]}