Teaching Domain and Range in Algebra 1 - Maneuvering the Middle - Free Printable

Let’s go through each problem one by one. For each set of ordered pairs, we need to:

1. Find the Domain → That’s all the x-values (first numbers in each pair).
2. Find the Range → That’s all the y-values (second numbers in each pair).
3. Decide if it’s a function → A relation is a function if NO x-value repeats with a different y-value. In other words, each x can only be paired with ONE y.

We’ll list domain and range as sets (no duplicates), and check for repeated x-values.

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

- Domain: x-values → -9, 8, -9, 3, 7 → remove duplicate → {-9, 3, 7, 8}
- Range: y-values → -8, -9, 5, 8, 8 → remove duplicate → {-9, -8, 5, 8}
- Function? → Look at x = -9: it appears twice — once with y=-8, once with y=5 → NOT a function.

✔ Final Answer for #1:
Domain: {-9, 3, 7, 8}
Range: {-9, -8, 5, 8}
Function?: No

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

- Domain: -7, 8, 3, 1, 4 → all unique → {-7, 1, 3, 4, 8}
- Range: 7, 5, -4, 0, -7 → all unique → {-7, -4, 0, 5, 7}
- Function? → All x-values are different → YES, it’s a function.

✔ Final Answer for #2:
Domain: {-7, 1, 3, 4, 8}
Range: {-7, -4, 0, 5, 7}
Function?: Yes

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

- Domain: 1, 3, 8, -6, -8 → all unique → {-8, -6, 1, 3, 8}
- Range: -2, 9, 6, 4, 4 → remove duplicate → {-2, 4, 6, 9}
- Function? → All x-values are different → YES.

✔ Final Answer for #3:
Domain: {-8, -6, 1, 3, 8}
Range: {-2, 4, 6, 9}
Function?: Yes

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

- Domain: 5, 2, -9, 3, -1 → all unique → {-9, -1, 2, 3, 5}
- Range: 2, 2, -8, -3, -7 → remove duplicate → {-8, -7, -3, 2}
- Function? → All x-values different → YES.

✔ Final Answer for #4:
Domain: {-9, -1, 2, 3, 5}
Range: {-8, -7, -3, 2}
Function?: Yes

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

- Domain: -7, 9, 3, 6, 6 → remove duplicate → {-7, 3, 6, 9}
- Range: 3, 4, -7, -4, -1 → all unique → {-7, -4, -1, 3, 4}
- Function? → x = 6 appears twice: with y=-4 and y=-1 → NOT a function.

✔ Final Answer for #5:
Domain: {-7, 3, 6, 9}
Range: {-7, -4, -1, 3, 4}
Function?: No

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

- Domain: -6, 6, -1, 9, -8 → all unique → {-8, -6, -1, 6, 9}
- Range: -8, 1, -8, 4, 2 → remove duplicate → {-8, 1, 2, 4}
- Function? → All x-values different → YES.

✔ Final Answer for #6:
Domain: {-8, -6, -1, 6, 9}
Range: {-8, 1, 2, 4}
Function?: Yes

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

- Domain: 5, -2, -5, 8, -1 → all unique → {-5, -2, -1, 5, 8}
- Range: -5, -4, -7, 8, -2 → all unique → {-7, -5, -4, -2, 8}
- Function? → All x-values different → YES.

✔ Final Answer for #7:
Domain: {-5, -2, -1, 5, 8}
Range: {-7, -5, -4, -2, 8}
Function?: Yes

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

- Domain: 8, -4, 1, -4, -6 → remove duplicate → {-6, -4, 1, 8}
- Range: 1, -2, 6, 9, -3 → all unique → {-3, -2, 1, 6, 9}
- Function? → x = -4 appears twice: with y=-2 and y=9 → NOT a function.

✔ Final Answer for #8:
Domain: {-6, -4, 1, 8}
Range: {-3, -2, 1, 6, 9}
Function?: No

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

- Domain: -4, 8, -7, -4, -9 → remove duplicate → {-9, -7, -4, 8}
- Range: -4, 9, 0, 3, 0 → remove duplicate → {-4, 0, 3, 9}
- Function? → x = -4 appears twice: with y=-4 and y=3 → NOT a function.

✔ Final Answer for #9:
Domain: {-9, -7, -4, 8}
Range: {-4, 0, 3, 9}
Function?: No

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

- Domain: -7, 8, -7, -9, -4 → remove duplicate → {-9, -7, -4, 8}
- Range: 9, -2, -4, 8, 7 → all unique → {-4, -2, 7, 8, 9}
- Function? → x = -7 appears twice: with y=9 and y=-4 → NOT a function.

✔ Final Answer for #10:
Domain: {-9, -7, -4, 8}
Range: {-4, -2, 7, 8, 9}
Function?: No

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Final Answer:

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