How do you find the domain and range of #y=1/(x-4)#?

1 Answer
Jun 25, 2015

Answer:

The only restriction on the domain is #x!=4#
As this would make the numerator #=0#

Explanation:

As #x# nears #4# from above, #y# will be larger and larger, or in "the language":
#lim_(x->4+) y = oo#
Something like that goes if #x# nears #4# from below:
#lim_(x->4-) y = -oo#
#x=4# is called the vertical asymptote.

#y# can never reach the value of #0# ( horizontal asymptote), so th range is #y!=0#, or:
#lim_(x->oo) y=0#

graph{1/(x-4) [-5.04, 14.96, -4.24, 5.76]}