Analyse the following two relations and explain which one is a function. Justify your reasoning with reference to the definition of a function: - Relation A: (1, 2), (2, 3), (3, 4), (4, 5) - Relation B: (1, 2), (1, 3), (2, 4), (3, 5) Consider a real-world scenario: A school assigns each student to a form class. Evaluate whether this mapping is a function. Explain your reasoning and discuss what would happen if a student were assigned to two form classes. Investigate the relationship between the domain and range in the mapping y = x². Explain why the range is different from the co-domain and what this tells us about the function. Given the mapping that connects each country to its capital city, analyse whether this is a one-to-one function. Justify your answer and explain the implications if a country had two capitals. A teacher creates a mapping where each learner is mapped to their test score. Evaluate whether this is a function. Discuss what would change if a learner took the test twice and received different scores. Analyse the following arrow diagram and determine all possible types of relations it could represent. Justify why some classifications are valid and others are not: - Domain: A, B, C - Co-domain: 1, 2, 3, 4 - A → 1, B → 2, C → 3 Explain why every function is a relation, but not every relation is a function. Use specific examples to support your explanation. Consider the mapping of students to their hobbies. Discuss whether this mapping is more likely to be one-to-many or many-to-many in a real school setting. Justify your reasoning. Evaluate the following statement: “If a relation is many-to-one, it cannot be a function.” Is this statement true or false? Provide evidence to support your answer. A company maps each employee to their salary. Analyse whether this is a function. Discuss what would happen if two employees had the same salary and explain the implications for the mapping.

Analyse the following two relations and explain which one is a function. Justify your reasoning with reference to the definition of a function: - Relation A: (1, 2), (2, 3), (3, 4), (4, 5) - Relation B: (1, 2), (1, 3), (2, 4), (3, 5) Step 1: Analyze Relation A. Relation A is (1, 2), (2, 3), (3, 4), (4, 5). In this relation, each element from the domain (the first element of each ordered pair) is mapped to exactly one element in the co-domain (the second element). • 1 is mapped only to 2. • 2 is mapped only to 3. • 3 is mapped only to 4. • 4 is mapped only to 5. Since every input has exactly one output, Relation A satisfies the definition of a function. Step 2: Analyze Relation B. Relation B is (1, 2), (1, 3), (2, 4), (3, 5). In this relation, the element 1 from the domain is mapped to two different elements in the co-domain: 2 and 3. • 1 is mapped to 2. • 1 is also mapped to 3. Since the input 1 has more than one output, Relation B does not satisfy the definition of a function. Step 3: Conclude which relation is a function. Based on the analysis, Relation A is a function because each element in its domain is associated with exactly one element in its co-domain. Relation B is not a function because the domain element 1 is associated with two different co-domain elements (2 and 3). Relation A is a function --- What's next?