Y=1/3x + 2 what is the domain?

To find the domains you must graph this equation and find the x-coordinates of the points plotted. That's the domain.

Remember, if two points have the same x-coordinate then do not repeat the number when stating the domain. Domain also always must be written in the least to greatest order. Domains must be written with {} enclosing them.

So if the x-coordinates were 4,5,6,4,7,5

You would write the domain as {4,5,6,7}

The denominator of y cannot be zero as this would make y
undefined
.
Equating the denominator to zero and solving gives the value that x cannot be.
solve
3
x
−
2
=
0
⇒
x
=
2
3
←
excluded value
⇒
domain is
x
∈
R
,
x
≠
2
3
Rearrange to make x the subject
y
(
3
x
−
2
)
=
1
⇒
3
x
y
−
2
y
=
1
⇒
3
x
y
=
1
+
2
y
⇒
x
=
1
+
2
y
3
y
solve
3
y
=
0
⇒
y
=
0
←
excluded value
⇒
range is
y
∈
R
,
y
≠
0

graph{1/(3x-2) [-10, 10, -5, 5]}