Identify Domain and Range of a Graph
-7 on the x- axis
1. Begin identifying the minimum and
maximum x-coordinate. Travel along the
x-axis going to the left of the origin, until
you are under the closed circle. The
x-coordinate is -7. The graph does not go
beyond -7, so -7 is the minimum
x-coordinate. Because it is a closed circle,7 is included in the domain.
2. Now travel to the right of the origin along
the x-axis. As you can see, the graph has an
arrow which indicates that it continues
forever in the positive x’s (remember we are
only looking at the x- axis/x-coordinate)
3. The domain would be {𝑥 | 𝑥 ≥ −7}
We use the greater than or equal to symbol
because the circle was closed.
4. Now identify the minimum and maximum
y-coordinate. Travel down the y-axis to find
the minimum y-coordinate. Since the graph
continues on into infinity, there is an infinite
number of minimum y’s.
5. Next find the maximum y-coordinate. The
highest y-value would be 6.
6. The range would be: {𝑦|𝑦 ≤ 6}.
All the y- values are less than or equal to 6
1 Find the minimum and maximum xcoordinate. Travel left along the xaxis until you are under the open
circle. This is an endpoint, the graph
stops or terminates. The minimum xcoordinate is –4
2. Now find the maximum xcoordinate. Travel to the right along
the x-axis until you are under the
closed circle. The graph terminates at
the closed circle. The maximum xcoordinate will be 6.
3. The graph has endpoints, so when
identifying the domain, the x will be
in the middle.
Domain: {𝑥| − 4 < 𝑥 ≤ 6}
min
max
4. Now identify the minimum and
maximum y-coordinates. Travel down
the y-axis to locate the minimum ycoordinate.
5. Next identify the maximum ycoordinate. The highest y-value would
be 5.
6. The graph has endpoints, so when
identifying the range, the y will be
in the middle.
Range: {𝑦| − 4 < 𝑦 ≤ 5}
min
max
1 Find the minimum and maximum xcoordinate. Travel left along the x-axis until
you are under the closed circle. This is an
endpoint, the graph stops or terminates.
The minimum x- coordinate is –7
2. Now find the maximum x- coordinate.
Travel to the right along the x-axis until you
are under the closed circle. The graph
terminates at the closed circle. The
maximum x- coordinate will be 7.
3. Since we can only go so far to the left
and right on the x-axis, the graph terminates.
The x will be in the middle due to endpoints.
Domain: {𝑥| − 7 ≤ 𝑥 ≤ 7 }
4. Now identify the minimum and
maximum y-coordinates. Travel down
the y-axis to locate the minimum y coordinate. The minimum ycoordinate is -3
5. Now identify the maximum y-coordinate.
Travel up the y-axis to the maximum point
on the graph. The maximum y value is 6.
6. Range: {𝑦| − 3 ≤ 𝑦 ≤ 6}
1 Find the minimum and maximum xcoordinate. Travel left along the x-axis until
you are under the closed circle. This is an
endpoint, the graph stops or terminates.
The minimum x- coordinate is –8.
2. Now find the maximum x- coordinate.
Travel to the right along the x-axis until you
are under the closed circle. The graph
terminates at the closed circle. The
maximum x- coordinate will be 5.
3. Domain {𝑥| − 8 ≤ 𝑥 < 5}
4. Now identify the minimum and
maximum y-coordinates. Notice that we can
only go up on the y-axis 2 units. This is true for
every point on the graph. So the range is y = 2
5. Range: {𝑦|𝑦 = 2}
YOU TRY IT
Domain:
Range: