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Identifying Functions - Worksheet 9 - 8th Grade

Hard

Connect functions with inputs, outputs, equations, slopes and coordinate graphs.

hard: Use another set to practice explaining and checking your answers.

27 problems · 15-20 minutes · Skills: functions, vertical line test, relations

About This Worksheet

This hard-level worksheet contains 27 problems designed for 8th Grade students practicing identifying functions. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Read ordered pairs and solve linear equations using signed arithmetic.

  • Connect functions with inputs, outputs, equations, slopes and coordinate graphs.
  • Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: Does the relation {(-2, 1), (-1, 3), (0, 4)} define y as a function of x? Explain.
Solution Steps:
  1. Look for an input paired with more than one different output.
  2. Repeated outputs are allowed; conflicting outputs for one input are not.
Answer: Yes; each input has exactly one output.
Tip: Check your result using the method in the example before moving to the next question.
1
Does the relation {(4, -2), (5, 0), (6, 1)} define y as a function of x? Explain.
2
Does the relation {(-1, -1), (0, 1), (-1, 2)} define y as a function of x? Explain.
3
Does the relation {(-4, 2), (-3, 4), (-2, 5)} define y as a function of x? Explain.
4
Does the relation {(4, 2), (5, 4), (4, 5)} define y as a function of x? Explain.
5
Does the relation {(-4, 0), (-3, 2), (-2, 3)} define y as a function of x? Explain.
6
Does the relation {(0, -2), (1, 0), (0, 1)} define y as a function of x? Explain.
7
Does the relation {(2, 1), (3, 3), (4, 4)} define y as a function of x? Explain.
8
Does the relation {(4, 0), (5, 2), (4, 3)} define y as a function of x? Explain.
9
Does the relation {(-1, -1), (0, 1), (1, 2)} define y as a function of x? Explain.
10
Does the relation {(2, 1), (3, 3), (2, 4)} define y as a function of x? Explain.
11
Does the relation {(4, 0), (5, 2), (6, 3)} define y as a function of x? Explain.
12
Does the relation {(-4, 0), (-3, 2), (-4, 3)} define y as a function of x? Explain.
13
Does the relation {(0, 2), (1, 4), (2, 5)} define y as a function of x? Explain.
14
Does the relation {(-4, 1), (-3, 3), (-4, 4)} define y as a function of x? Explain.
15
Does the relation {(3, 1), (4, 3), (5, 4)} define y as a function of x? Explain.
16
Does the relation {(0, -1), (1, 1), (0, 2)} define y as a function of x? Explain.
17
Does the relation {(-4, -1), (-3, 1), (-2, 2)} define y as a function of x? Explain.
18
Does the relation {(-2, 1), (-1, 3), (-2, 4)} define y as a function of x? Explain.
19
Does the relation {(-3, 2), (-2, 4), (-1, 5)} define y as a function of x? Explain.
20
Does the relation {(-3, -1), (-2, 1), (-3, 2)} define y as a function of x? Explain.
21
Does the relation {(3, -1), (4, 1), (5, 2)} define y as a function of x? Explain.
22
Does the relation {(4, -2), (5, 0), (4, 1)} define y as a function of x? Explain.
23
Does the relation {(2, -1), (3, 1), (4, 2)} define y as a function of x? Explain.
24
Does the relation {(-4, -2), (-3, 0), (-4, 1)} define y as a function of x? Explain.
25
Does the relation {(1, 1), (2, 3), (3, 4)} define y as a function of x? Explain.
26
Does the relation {(-3, 0), (-2, 2), (-3, 3)} define y as a function of x? Explain.
27
Does the relation {(-1, 2), (0, 4), (1, 5)} define y as a function of x? Explain.

Answer Key

1. Yes; each input has exactly one output.2. No; input -1 has two different outputs.3. Yes; each input has exactly one output.4. No; input 4 has two different outputs.5. Yes; each input has exactly one output.6. No; input 0 has two different outputs.7. Yes; each input has exactly one output.8. No; input 4 has two different outputs.9. Yes; each input has exactly one output.10. No; input 2 has two different outputs.11. Yes; each input has exactly one output.12. No; input -4 has two different outputs.13. Yes; each input has exactly one output.14. No; input -4 has two different outputs.15. Yes; each input has exactly one output.16. No; input 0 has two different outputs.17. Yes; each input has exactly one output.18. No; input -2 has two different outputs.19. Yes; each input has exactly one output.20. No; input -3 has two different outputs.21. Yes; each input has exactly one output.22. No; input 4 has two different outputs.23. Yes; each input has exactly one output.24. No; input -4 has two different outputs.25. Yes; each input has exactly one output.26. No; input -3 has two different outputs.27. Yes; each input has exactly one output.

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What skills does this functions worksheet cover?

This worksheet focuses on functions, vertical line test, relations. It is designed for 8th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

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How many problems are on this worksheet?

This worksheet contains 27 problems. It typically takes 15-20 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.