Hey guys! Here are some questions on relations and functions. For guidance through the questions just remember the below terms and their definitions.

**Relations**: A relation is a set of one or more ordered pairs.

**Functions**: A function is a relation in which each element of the domain is paired with EXACTLY one element of the range.

**The Vertical Line Test**: Given the graph of a relation, if a vertical line can be drawn that crosses the graph in more than one place, then the relation is not a function.

### Let’s get started!

**Q1. Using the vertical line test, determine if the graph above shows a relation, a function, both a relation and afunction, or neither a relation nor a function.A. neither a relation nor a functionB. relation onlyC. both a relation and a functionD. function only**

Solution: To check if a given graph represents a function or not, we use The Vertical Line Test. The above graph does not pass the Vertical Line Test as every vertical line cuts the graph more than 2 times. Hence it represents ** relation only**.

**Q2. Which of these graphs represents a function?**

Solution: In the above graphs, only **graph Y** represents a function as it passes the vertical line test. In graph Y, each vertical line goes through the graph only one time.

**Q3. Which of these t-tables represents a function?**

Solution: In the above t-tables, **table Y** represents a function as in a function, each value of domain( f(x) ) is paired with exactly one element in the range(x). In other tables, two values of the domain are paired with the same value in range.

**Q4 . Which of these graphs represents a function?**

Solution: In the above graphs, **graph Y **represents a function as it passes the Vertical Line Test. In graph Y, each vertical line goes through the graph only once but in other graphs, each vertical line goes through the graph more than once.

**Q5. Which of the following relations describes a function?A. { (0, 0), (0, 2), (2, 0), (2, 2) }B. { (2, 2), (2, 3), (3, 2), (3, 3) }C. { (2, -1), (2, 1), (3, -1), (3, 1) }D.{ (-2, -3), (-3, -2), (2, 3), (3, 2) }**

Solution: In the above relations, **relation D **represents a function as in relation D, each value of domain(X) is paired with exactly one element in range(y), but in other relations, each value of the domain is paired with two or more elements in the range.

**Q6. Do the ordered pairs below represent a relation, a function, both a relation and a function, or neither a relation nor a function?**

**(-2,-1) , (1,-4) , (7,-10) , (8,-11)**

**A. neither a relation nor a functionB. both a relation and a functionC. relation onlyD. function only**

Solution: Here we have to plot a graph take above pairs as coordinates.

As the graph has passed the vertical line test, hence the given relation represents both a relation and a function.

**Q7. Determine whether this picture is an example of a function, relation, function, and relation, or neither relationnor function.A. function and relationB. function onlyC. relation onlyD. neither function nor relation**

Solution: The given graph represent **only relation** as it does not passes the Vertical Line Test. In the given graph every vertical line passes the graph more than once hence it doesn’t represent a function.

**Q8. Which relation diagram represents a function?**

Solution: In the above diagrams, **diagram W **represents a function as in diagram W, every domain element (input) is paired with exactly one of the range (output) element.

**Q9. Which of the following relations describes a function?A. { (2, 2), (3, 2), (4, 2), (5, 2) }B. { (-2, 0), (0, -2), (0, 2), (2, 0) }C. { (0, 0), (2, -2), (2, 2), (3, 3) }D. { (2, 3), (2, 4), (2, 5), (2, 6) }**

Solution: In the above relations, **relation A **represents a function as in relation D, each value of domain(X) is paired with exactly one element in range(y), but in other relations, each value of the domain is paired with two or more elements in the range.

**Q10. Which of these graphs represents a function?**

Solution: In the above graphs, **graph Y **represents a function as it passes the Vertical Line Test. In graph Y, each vertical line goes through the graph only once but in other graphs, each vertical line goes through the graph more than once. Graph X also doesn’t represent a function because for it’s each value of X(domain), it has infinite Y (range) values.

**Q11. Which relation diagram represents a function?**

Solution: In the above diagrams, **diagrams W **represents a function as in the diagram W, each value of domain(input) is paired with exactly one (or same) element in range(output), but in other diagrams, each value of the domain is paired with two or more elements in the range.

**Q12. Which of the following relations describes a function?A. { (0, 0), (1, -1), (1, 1), (2, 2) }B. { (-2, 2), (-1, -1), (-1, 1), (0, 0) }C. { (-1, 0), (0, 1), (1, 0), (0, -1) }D. { (-2, 2), (-1, 1), (1, 1), (2, 2) }**

Solution: In the above relations, **relation D **represents a function as in relation D, each value of domain(X) is paired with exactly one element in range(y), but in other relations, each value of the domain is paired with two or more elements in the range.

**Q13. Which of these mappings is a function?**

Solution: In the above mappings, **mapping Z **represents a function as in the mapping Z, each value of domain(X) is paired with exactly one element in range( f(x) ), but in other diagrams, each value of the domain is paired with two or more elements in the range.

**Q14. Which of these graphs represents a function?**

Solution: In the above graphs, **graph Z **represents a function as it passes the Vertical Line Test. In graph Z, each vertical line goes through the graph only once but in other graphs, each vertical line goes through the graph more than once. Graph Y also doesn’t represent a function because for it’s each value of X(domain), it has infinite Y (range) values.

**Q15. Which of these mappings is a function?**

Solution: In the above mappings, **mapping Z **represents a function as in the mapping Z, each value of domain(X) is paired with exactly one element in range( f(x) ), but in other diagrams, each value of the domain is paired with two or more elements in the range.

**Q16. Which of the following represents a relation and not a function?**

**A. { (-10, 34), (-6, 32), (-10, 40), (1,34) }B. { (-10, 34), (-6, 32), (-2, 40), (1,34) }C. { (-10, 34), (-6,32), (6, 40), (12, 34) }D. { (6, 34), (-6, 32), (12, 40), (-10, 34) }**

Solution: In the above relations, **relation A **represents not a function as in relation A, it’s 2 range values are paired with its one domain value i.e. (-10)

**Q17. Think about the vertical line test and answer the following question. Would a vertical line be a relation, a function, both a relation and a function, or neither a relation nor a function?A. function onlyB. both a relation and a functionC. neither a relation nor a functionD. relation only**

Solution: The graph with a vertical line represent a **relation only**. It doesn’t represent a function because for it’s each value of X(domain), it has infinite Y (range) values.

**Q18. Which of the following graphs is not a function?**

Solution: In the above graphs, **graph Z **does not represent a function as it does not passes the Vertical Line Test. In graph Z, each vertical line goes through the graph more than once but in other graphs, each vertical line goes through the graph only once.

**Q19. Which of these t-tables represents a function?**

Solution: In the above t-tables, **table Y** represents a function as in a function, each value of domain( f(x) ) is paired with exactly one element in the range(x). In other tables, two values of the domain are paired with the same value in range.

**Q20. Which of the following relations describes a function?A. { (-3, 9), (-2, 4), (2, 4), (3, 9) }B. { (2, -2), (0, 0), (2, 2), (3, 3) }C. { (-2, 0), (0, 2), (2, 0), (0, -2) }D. { (9, -3), (4, -2), (4, 2), (9, 3) }**

Solution: In the above relations, **relation A **represents a function as in relation A, each value of domain(X) is paired with exactly one element in range(y), but in other relations, each value of the domain is paired with two or more elements in the range.

**Q21. Which of the following graphs is not a function?**

Solution: In the above graphs, **graph Z **does not represent a function as it does not passes the Vertical Line Test. In graph Z, each vertical line goes through the graph more than once but in other graphs, each vertical line goes through the graph only once.

**Q22. Which relation diagram represents a function?**

Solution: In the above diagrams, **diagrams X **represents a function as in diagram X, each value of domain(input) is paired with exactly one (or same) element in range(output), but in other diagrams, each value of the domain is paired with two or more elements in the range.

**Q23. Determine whether this picture is an example of a function, relation, function and relation, or neither relation nor function.**

Solution: To check if a given graph represents a function or not, we use The Vertical Line Test. The above graph does not pass the Vertical Line Test as every vertical line cuts the graph more than 2 times. Hence it represents ** relation only**.

**Q24. Do the ordered pairs below represent a relation, a function, both a relation and a function, or neither a relation nor a function?**

**(-4,-3) , (1,-8) , (-4,-14) , (9,-16)**

**A. function onlyB. both a relation and a functionC. neither a relation nor a functionD. relation only**

Solution: Here we have to plot a rough graph take above pairs as coordinates.

As the graph has passed the vertical line test, hence the given relation represents both a relation and a function.

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