# What is the domain and range of #(x-1)/(x-4)#?

##### 1 Answer

Domain:

Range:

#### Explanation:

The domain of the function will include all possible value of **except** the value that makes the denominator equal to zero. More specifically,

To determine the range of the function, you can do a little algebraic manipulation to rewrite the function as

#y = ((x - 4) + 3)/(x-4) = 1 + 3/(x-4)#

Since the fraction **never** be equal to zero, the function can never take the value

#y = 1 + 0 = 1#

This means that the range of the function will be

graph{(x-1)/(x-4) [-18.8, 21.75, -10.3, 9.98]}