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

1 Answer
Aug 29, 2015

Answer:

Domain: #(-oo, 4) uu (4, + oo)#
Range: #(-oo, 1) uu (1, + oo)#

Explanation:

The domain of the function will include all possible value of #x# except the value that makes the denominator equal to zero. More specifically, #x=4# will be excluded from the domain, which will thus be #(-oo, 4) uu (4, + oo)#.

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 #3/(x-4)# can 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 #(-oo, 1) uu (1, + oo)#.

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