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

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