What is the domain and range of #(x^3-8)/(x^2-5x+6)#?

1 Answer
Feb 2, 2016

Answer:

The domain is the set of all real values of x except #2# and #3#

The range is the set of all real values of #y#.

Explanation:

The domain of a function is the set of #x# values for which the function is valid. The range is the corresponding set of #y# values.

#(x^3 - 8)/(x^2 - 5x +6)#

#=((x-2)(x^2 +2x +4))/((x-3)(x-2)#

Thus there is a removable vertical asymptote at #x=2# and another vertical asymptote at #x=3# because both of these values would make the denominator equal to zero.

The domain is the set of all real values of x except #2# and #3#

The range is the set of all real values of #y#.