Algebra 1 Worksheets | Domain and Range Worksheets - Free Printable

Let's solve each problem step by step.

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Definitions:

- Domain: The set of all x-values (first numbers in the ordered pairs).
- Range: The set of all y-values (second numbers in the ordered pairs).
- Function?: A relation is a function if each x-value appears only once (no repeated x-values). If any x-value repeats with different y-values, it's not a function.

We will go through each set:

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1) {(-9, -8), (8, -9), (-9, 5), (3, 8), (7, 8)}

- Domain: {-9, 8, 3, 7} → But wait! -9 appears twice: (-9, -8) and (-9, 5)
- Range: {-8, -9, 5, 8}
- Function? ✘ No — because x = -9 maps to two different y-values.
- ✔ Answer:
- Domain: {-9, 8, 3, 7}
- Range: {-8, -9, 5, 8}
- Function? No

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2) {(-7, 7), (8, 5), (-3, -4), (1, 0), (4, -7)}

- All x-values are unique: -7, 8, -3, 1, 4
- Domain: {-7, 8, -3, 1, 4}
- Range: {7, 5, -4, 0, -7}
- Function? ✔ Yes — no repeated x-values
- ✔ Answer:
- Domain: {-7, 8, -3, 1, 4}
- Range: {7, 5, -4, 0, -7}
- Function? Yes

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3) {(1, -2), (3, 9), (8, 6), (-6, 4), (-8, 4)}

- All x-values: 1, 3, 8, -6, -8 → all unique
- Domain: {1, 3, 8, -6, -8}
- Range: {-2, 9, 6, 4} → note: 4 appears twice, but that’s okay for range
- Function? ✔ Yes — no repeated x-values
- ✔ Answer:
- Domain: {1, 3, 8, -6, -8}
- Range: {-2, 9, 6, 4}
- Function? Yes

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4) {(5, 2), (2, 2), (-9, -8), (-3, -3), (-1, -7)}

- x-values: 5, 2, -9, -3, -1 → all unique
- Domain: {5, 2, -9, -3, -1}
- Range: {2, -8, -3, -7} → note: 2 appears twice, but that’s fine
- Function? ✔ Yes — no repeated x-values
- ✔ Answer:
- Domain: {5, 2, -9, -3, -1}
- Range: {2, -8, -3, -7}
- Function? Yes

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5) {(-7, 3), (9, 4), (3, -7), (6, -4), (6, -1)}

- x-values: -7, 9, 3, 6, 6 → 6 appears twice
- (6, -4) and (6, -1) → same x, different y
- Domain: {-7, 9, 3, 6}
- Range: {3, 4, -7, -4, -1}
- Function? ✘ No — x = 6 has two different outputs
- ✔ Answer:
- Domain: {-7, 9, 3, 6}
- Range: {3, 4, -7, -4, -1}
- Function? No

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6) {(-6, -8), (6, 1), (-1, -8), (9, 4), (-8, 2)}

- x-values: -6, 6, -1, 9, -8 → all unique
- Domain: {-6, 6, -1, 9, -8}
- Range: {-8, 1, 4, 2} → -8 appears twice, but okay
- Function? ✔ Yes — no repeated x-values
- ✔ Answer:
- Domain: {-6, 6, -1, 9, -8}
- Range: {-8, 1, 4, 2}
- Function? Yes

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7) {(5, -5), (-2, -4), (-5, -7), (8, 8), (-1, -2)}

- x-values: 5, -2, -5, 8, -1 → all unique
- Domain: {5, -2, -5, 8, -1}
- Range: {-5, -4, -7, 8, -2}
- Function? ✔ Yes
- ✔ Answer:
- Domain: {5, -2, -5, 8, -1}
- Range: {-5, -4, -7, 8, -2}
- Function? Yes

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8) {(8, 1), (-4, -2), (1, 6), (-4, 9), (-6, -3)}

- x-values: 8, -4, 1, -4, -6 → -4 appears twice
- (-4, -2) and (-4, 9) → same x, different y
- Domain: {8, -4, 1, -6}
- Range: {1, -2, 6, 9, -3}
- Function? ✘ No
- ✔ Answer:
- Domain: {8, -4, 1, -6}
- Range: {1, -2, 6, 9, -3}
- Function? No

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9) {(-4, -4), (8, 9), (-7, 0), (-4, 3), (-9, 0)}

- x-values: -4, 8, -7, -4, -9 → -4 appears twice
- (-4, -4) and (-4, 3) → same x, different y
- Domain: {-4, 8, -7, -9}
- Range: {-4, 9, 0, 3}
- Function? ✘ No
- ✔ Answer:
- Domain: {-4, 8, -7, -9}
- Range: {-4, 9, 0, 3}
- Function? No

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10) {(-7, 9), (8, -2), (-7, -4), (-9, 8), (-4, 7)}

- x-values: -7, 8, -7, -9, -4 → -7 appears twice
- (-7, 9) and (-7, -4) → same x, different y
- Domain: {-7, 8, -9, -4}
- Range: {9, -2, -4, 8, 7}
- Function? ✘ No
- ✔ Answer:
- Domain: {-7, 8, -9, -4}
- Range: {9, -2, -4, 8, 7}
- Function? No

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✔ Final Answers Summary:

| Problem | Domain | Range | Function? |
|--------|--------|-------|----------|
| 1) | {-9, 8, 3, 7} | {-8, -9, 5, 8} | No |
| 2) | {-7, 8, -3, 1, 4} | {7, 5, -4, 0, -7} | Yes |
| 3) | {1, 3, 8, -6, -8} | {-2, 9, 6, 4} | Yes |
| 4) | {5, 2, -9, -3, -1} | {2, -8, -3, -7} | Yes |
| 5) | {-7, 9, 3, 6} | {3, 4, -7, -4, -1} | No |
| 6) | {-6, 6, -1, 9, -8} | {-8, 1, 4, 2} | Yes |
| 7) | {5, -2, -5, 8, -1} | {-5, -4, -7, 8, -2} | Yes |
| 8) | {8, -4, 1, -6} | {1, -2, 6, 9, -3} | No |
| 9) | {-4, 8, -7, -9} | {-4, 9, 0, 3} | No |
| 10) | {-7, 8, -9, -4} | {9, -2, -4, 8, 7} | No |

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✔ Key Tip: Always check for repeated x-values. If any x appears more than once with different y-values, it's not a function. If the same x has the same y, it's still okay (but rare).

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