How do you find the domain and range and determine whether the relation is a function given :#y=3x-4#?

1 Answer
Apr 20, 2017

Answer:

See below

Explanation:

The domain is #RR# since the relation is well defined for all #x in RR#.
The codomain is also #RR# since for every #y_0 in RR# we can take #x_0=1/3y_0+4/3# and get that

#3x_0-4=3(1/3y_0+4/3)-4=y_0#

The relation is a function:

EXISTENCE:

for every #x# in the domain (#RR#) there is #y# in the codomain (#RR#) such that #y=3x+1#: trivial, just take #y=3x+1#.

UNIQUENESS:

If #y_1# and #y_2# are images of the same #x_0#, then

#y_1 - y_2=3x_0+4 - 3x_0-4=0 Rightarrow y_1 = y_2#