Domain and range worksheet with ordered pairs and graphing exercises.

Let’s solve each part step by step.

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Part A: Find domain and range of each relation (ordered pairs)

Remember:
- Domain = all the x-values (first numbers in the pairs)
- Range = all the y-values (second numbers in the pairs)
- List them without repeating, usually from smallest to largest.

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

x-values: 3, -1, 0, 7 → Domain: {-1, 0, 3, 7}
y-values: -2, 4, 5, -2 → Range: {-2, 4, 5} *(don’t repeat -2)*

✔ Domain: {-1, 0, 3, 7}
✔ Range: {-2, 4, 5}

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2. {(-8, 1), (-6, 2), (-4, 3), (-2, 4), (0, 5)}

x-values: -8, -6, -4, -2, 0 → Domain: {-8, -6, -4, -2, 0}
y-values: 1, 2, 3, 4, 5 → Range: {1, 2, 3, 4, 5}

✔ Domain: {-8, -6, -4, -2, 0}
✔ Range: {1, 2, 3, 4, 5}

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3. {(5, 10), (6, 12), (7, 14), (8, 16), (9, 18)}

x-values: 5, 6, 7, 8, 9 → Domain: {5, 6, 7, 8, 9}
y-values: 10, 12, 14, 16, 18 → Range: {10, 12, 14, 16, 18}

✔ Domain: {5, 6, 7, 8, 9}
✔ Range: {10, 12, 14, 16, 18}

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4. {(2, 3), (4, 5), (6, 7), (8, 9), (10, 11)}

x-values: 2, 4, 6, 8, 10 → Domain: {2, 4, 6, 8, 10}
y-values: 3, 5, 7, 9, 11 → Range: {3, 5, 7, 9, 11}

✔ Domain: {2, 4, 6, 8, 10}
✔ Range: {3, 5, 7, 9, 11}

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5. {(1, 2), (3, 4), (5, 6), (7, 8), (9, 10)}

x-values: 1, 3, 5, 7, 9 → Domain: {1, 3, 5, 7, 9}
y-values: 2, 4, 6, 8, 10 → Range: {2, 4, 6, 8, 10}

✔ Domain: {1, 3, 5, 7, 9}
✔ Range: {2, 4, 6, 8, 10}

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6. {(0, 0), (1, 1), (2, 4), (3, 9), (4, 16)}

x-values: 0, 1, 2, 3, 4 → Domain: {0, 1, 2, 3, 4}
y-values: 0, 1, 4, 9, 16 → Range: {0, 1, 4, 9, 16}

✔ Domain: {0, 1, 2, 3, 4}
✔ Range: {0, 1, 4, 9, 16}

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7. {(-3, 9), (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4), (3, 9)}

x-values: -3, -2, -1, 0, 1, 2, 3 → Domain: {-3, -2, -1, 0, 1, 2, 3}
y-values: 9, 4, 1, 0, 1, 4, 9 → Range: {0, 1, 4, 9} *(remove duplicates)*

✔ Domain: {-3, -2, -1, 0, 1, 2, 3}
✔ Range: {0, 1, 4, 9}

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8. {(1, 1), (2, 8), (3, 27), (4, 64), (5, 125)}

x-values: 1, 2, 3, 4, 5 → Domain: {1, 2, 3, 4, 5}
y-values: 1, 8, 27, 64, 125 → Range: {1, 8, 27, 64, 125}

✔ Domain: {1, 2, 3, 4, 5}
✔ Range: {1, 8, 27, 64, 125}

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Part B: Graphs — find domain and range from plotted points

We look at the x-coordinates for domain, y-coordinates for range.

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9. Points on graph: Let’s read coordinates from grid.

Looking at graph 9:

Points appear to be:
(-3, 2), (-2, 0), (-1, -2), (0, 0), (1, 2), (2, 0), (3, -2)

Wait — let me double-check based on typical patterns. Actually, looking again:

From left to right:

At x = -3 → y = 2
x = -2 → y = 0
x = -1 → y = -2
x = 0 → y = 0
x = 1 → y = 2
x = 2 → y = 0
x = 3 → y = -2

So:

Domain: {-3, -2, -1, 0, 1, 2, 3}
Range: {-2, 0, 2} *(only unique y-values)*

✔ Domain: {-3, -2, -1, 0, 1, 2, 3}
✔ Range: {-2, 0, 2}

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10. Graph 10:

Points:
(-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)

Domain: {-2, -1, 0, 1, 2}
Range: {0, 1, 4}

✔ Domain: {-2, -1, 0, 1, 2}
✔ Range: {0, 1, 4}

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11. Graph 11:

Points:
(-3, -3), (-2, -1), (-1, 1), (0, 3), (1, 1), (2, -1), (3, -3)

Domain: {-3, -2, -1, 0, 1, 2, 3}
Range: {-3, -1, 1, 3}

✔ Domain: {-3, -2, -1, 0, 1, 2, 3}
✔ Range: {-3, -1, 1, 3}

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Now compiling final answers clearly.

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Final Answer:

A)
1. Domain: {-1, 0, 3, 7}; Range: {-2, 4, 5}
2. Domain: {-8, -6, -4, -2, 0}; Range: {1, 2, 3, 4, 5}
3. Domain: {5, 6, 7, 8, 9}; Range: {10, 12, 14, 16, 18}
4. Domain: {2, 4, 6, 8, 10}; Range: {3, 5, 7, 9, 11}
5. Domain: {1, 3, 5, 7, 9}; Range: {2, 4, 6, 8, 10}
6. Domain: {0, 1, 2, 3, 4}; Range: {0, 1, 4, 9, 16}
7. Domain: {-3, -2, -1, 0, 1, 2, 3}; Range: {0, 1, 4, 9}
8. Domain: {1, 2, 3, 4, 5}; Range: {1, 8, 27, 64, 125}

B)
9. Domain: {-3, -2, -1, 0, 1, 2, 3}; Range: {-2, 0, 2}
10. Domain: {-2, -1, 0, 1, 2}; Range: {0, 1, 4}
11. Domain: {-3, -2, -1, 0, 1, 2, 3}; Range: {-3, -1, 1, 3}