Sure! Let’s solve each problem step by step.
---
🔑 Key Concepts:
-
Domain: The set of all
x-values (first elements) in the ordered pairs.
-
Range: The set of all
y-values (second elements) in the ordered pairs.
-
Function?: A relation is a
function if
no x-value repeats with a different y-value. In other words, each input (x) must have
exactly one output (y).
---
Let’s go through each one:
---
1) { (9, -8), (8, -9), (-9, 5), (3, 8), (7, 8) }
-
Domain: {9, 8, -9, 3, 7}
-
Range: {-8, -9, 5, 8}
-
Function?:
✔ Yes — all x-values are unique.
---
2) { (-7, 7), (8, 5), (3, -4), (1, 0), (4, -7) }
-
Domain: {-7, 8, 3, 1, 4}
-
Range: {7, 5, -4, 0, -7}
-
Function?:
✔ Yes — all x-values are unique.
---
3) { (1, -2), (3, 9), (8, 6), (-6, 4), (-8, 4) }
-
Domain: {1, 3, 8, -6, -8}
-
Range: {-2, 9, 6, 4}
-
Function?:
✔ Yes — even though y=4 appears twice, it’s for different x-values (-6 and -8). That’s fine. Function only cares about x-values being unique.
---
4) { (5, 2), (2, 2), (-9, -8), (3, -3), (-1, -7) }
-
Domain: {5, 2, -9, 3, -1}
-
Range: {2, -8, -3, -7}
-
Function?:
✔ Yes — all x-values are unique.
---
5) { (-7, 3), (9, 4), (3, -7), (6, -4), (6, -1) }
-
Domain: {-7, 9, 3, 6} ← Note: 6 appears twice, but we list it once in domain.
-
Range: {3, 4, -7, -4, -1}
-
Function?:
✘ No — because x = 6 maps to two different y-values: -4 and -1. Violates function rule.
---
6) { (-6, -8), (6, 1), (-1, -8), (9, 4), (-8, 2) }
-
Domain: {-6, 6, -1, 9, -8}
-
Range: {-8, 1, 4, 2}
-
Function?:
✔ Yes — all x-values are unique.
---
7) { (5, -5), (-2, -4), (-5, -7), (8, 8), (-1, -2) }
-
Domain: {5, -2, -5, 8, -1}
-
Range: {-5, -4, -7, 8, -2}
-
Function?:
✔ Yes — all x-values are unique.
---
8) { (8, 1), (-4, -2), (1, 6), (-4, 9), (-6, -3) }
-
Domain: {8, -4, 1, -6} ← -4 appears twice
-
Range: {1, -2, 6, 9, -3}
-
Function?:
✘ No — x = -4 maps to both -2 and 9. Not allowed in a function.
---
9) { (-4, -4), (8, 9), (-7, 0), (-4, 3), (-9, 0) }
-
Domain: {-4, 8, -7, -9} ← -4 appears twice
-
Range: {-4, 9, 0, 3}
-
Function?:
✘ No — x = -4 maps to both -4 and 3. Not a function.
---
10) { (-7, 9), (8, -2), (-7, -4), (-9, 8), (-4, 7) }
-
Domain: {-7, 8, -9, -4} ← -7 appears twice
-
Range: {9, -2, -4, 8, 7}
-
Function?:
✘ No — x = -7 maps to both 9 and -4. Not a function.
---
##
✔ Final Answers:
| Problem | Domain | Range | Function? |
|---------|----------------------------|----------------------------|---------|
| 1 | {9, 8, -9, 3, 7} | {-8, -9, 5, 8} | Yes |
| 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 |
---
✔ Summary:
A relation is a function
only if each x-value appears once (i.e., no repeated x with different y). Even if y-values repeat, that’s okay — as long as each x has only one y.
Let me know if you’d like this formatted for printing or need a worksheet version!
Parent Tip: Review the logic above to help your child master the concept of function mapping worksheet.
