Domain and Range Worksheets - Free Printable

Let’s go through each graph one by one to find the domain and range.

Remember:
- Domain = all the x-values (left to right) that the graph covers.
- Range = all the y-values (bottom to top) that the graph covers.

We’ll look at each graph carefully, including whether endpoints are open circles (not included) or closed dots (included).

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Graph 1 (Top Left)

Graph goes from x = -5 to x = 2 → Domain: [-5, 2]
Y-values go from y = -3 to y = 4 → Range: [-3, 4]

✔ Both ends are solid dots → include them.

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Graph 2 (Top Middle)

Line starts at x = -6 (solid dot), ends at x = 3 (open circle) → Domain: [-6, 3)
Y-values: from y = -1 (at x=3, open) up to y = 5 (at x=-6, solid) → Range: (-1, 5]

Wait — let’s check direction. As x increases, y decreases. At x=-6, y=5. At x=3, y=-1 but it’s an open circle → so y never actually reaches -1.

So Range is from just above -1 up to 5 → (-1, 5]

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Graph 3 (Top Right)

Starts at x = -4 (solid dot), ends at x = 5 (solid dot) → Domain: [-4, 5]
Lowest point: y = -4 (at x=5), highest: y = 3 (at x=-4) → Range: [-4, 3]

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Graph 4 (Middle Left)

Vertical line? No — it’s a curve going from x = -4 to x = 2 → Domain: [-4, 2]
Y-values: lowest y = -5, highest y = 5 → Range: [-5, 5]

All points seem connected with no breaks → includes both ends.

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Graph 5 (Middle Center)

This one has two parts! One part from x = -4 to x = 0 (with open circle at x=0), then another from x=0 (open) to x=4.

But wait — at x=0, there’s an open circle on both sides? Actually, looking closely: left piece ends at (0, -2) open, right piece starts at (0, 2) open → so x=0 is NOT included.

So Domain: [-4, 0) ∪ (0, 4]

Now Range: Left piece goes from y=-5 to y=-2 (but not including -2). Right piece goes from y=2 to y=5 (not including 2). So combined range: [-5, -2) ∪ (2, 5]

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Graph 6 (Middle Right)

Curve from x = -5 to x = 5 → Domain: [-5, 5]
Lowest y = -3, highest y = 3 → Range: [-3, 3]

Ends are solid → include them.

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Graph 7 (Bottom Left)

Parabola opening down. Vertex at (0,4), crosses x-axis at x=-3 and x=3 → Domain: [-3, 3]
Max y = 4, min y = 0 (touches x-axis) → Range: [0, 4]

Solid dots at ends → include.

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Graph 8 (Bottom Middle)

Straight line from x = -5 to x = 3 → Domain: [-5, 3]
At x=-5, y=4; at x=3, y=-4 → since it’s straight and continuous, Range: [-4, 4]

Both ends solid → include.

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Graph 9 (Bottom Right)

U-shaped parabola. Starts at x = -4 (solid), ends at x = 4 (solid) → Domain: [-4, 4]
Minimum y = -3 (vertex), maximum y = 5 (ends) → Range: [-3, 5]

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Now let’s write final answers clearly for each:

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Final Answer:

1. Domain: [-5, 2], Range: [-3, 4]
2. Domain: [-6, 3), Range: (-1, 5]
3. Domain: [-4, 5], Range: [-4, 3]
4. Domain: [-4, 2], Range: [-5, 5]
5. Domain: [-4, 0) ∪ (0, 4], Range: [-5, -2) ∪ (2, 5]
6. Domain: [-5, 5], Range: [-3, 3]
7. Domain: [-3, 3], Range: [0, 4]
8. Domain: [-5, 3], Range: [-4, 4]
9. Domain: [-4, 4], Range: [-3, 5]