How do you find the domain and range of #y = (x+4 )/( x-4)#?

1 Answer
Oct 16, 2015

Answer:

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

Explanation:

The domain of the function will include all the values of #x# for which the denominator is not equal to zero.

This means that you have

#x - 4 = 0 implies x = 4#

This value of #x# will be excluded from the domain of the function. This implies that the function's domain will be #x in RR "\" {4}#, or #x in (-oo, 4) uu (4, + oo)#.

To find the range of the function, use some algebraic manipulation to rewrite the function as

#y = (x+4)/(x-4) = (x - 4 + 8)/(x-4) = 1 + 8/(x-4)#

Since #8/(x-4) !=0 AA x in (-oo, 4) uu (4, + oo)#, it follows that you can never have #y = 1#.

This means that the range of the function will be #x in RR "\" {1}#, or #x in (-oo, 1) uu (1, + oo)#.

graph{(x+4)/(x-4) [-9.99, 10.02, -5, 4.995]}