How do you find the domain and range of #y = 3/x^2#?

1 Answer
May 31, 2018

Answer:

Domain: #{x|x !=0}# or #(-oo, 0)uu(0,oo)#

Range: #{y|y>0}# or #(0, oo)#

Explanation:

#y = 3/x^2#

The function is undefined if the denominator is zero, so we set it equal to 0 and solve:

#x^2=0#

#x=+-sqrt0#

#x=0#

So the domain is:

#{x|x !=0}# or #(-oo, 0)uu(0,oo)#

Now as #x# gets close to #-oo# or #oo# the function gets closer to 0 but never actually gets to 0 and as #x# gets very close to 0 the function grows to #oo# so the range is:

#{y|y>0}# or #(0, oo)#

graph{y = 3/x^2 [-10, 10, -5, 5]}