Exploring Relations and Functions

1. Define a relation and provide an example.

• The sales data of a store, represented as {(Item1, 100), (Item2, 200)}.

• The relationship between a parent and child, like {(John, Sarah), (Emily, Tom)}.

• An example of a relation is the enrollment of students in courses, such as {(Alice, Math), (Bob, Science), (Alice, Science)}.

• The weather conditions in a city, such as {(New York, Rainy), (Los Angeles, Sunny)}.

2. What is the difference between a relation and a function?

• A relation is always a subset of a function.

• A function can have multiple outputs for a single input, while a relation has exactly one output for each input.

• A relation can have multiple outputs for a single input, while a function has exactly one output for each input.

• A function can have no outputs for an input, while a relation must have at least one output.

3. Determine if the following set is a function: {(1, 2), (2, 3), (1, 4)}.

• The set contains unique pairs only.

• The set is a function because it has two elements.

• Yes, the set is a function.

• No, the set is not a function.

4. Evaluate the composition of functions f(x) = 2x + 3 and g(x) = x^2. What is (f ∘ g)(2)?

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5. Find the domain of the function f(x) = 1/(x - 3).

• All real numbers

• Only positive numbers

• All real numbers except 0

• All real numbers except 3

6. Find the range of the function f(x) = x^2 - 4.

• (-∞, -4)

• (-4, 0)

• [-4, ∞)

• [0, 4]

7. If f(x) = 3x - 5, what is f(4)?

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• 1

8. Determine the inverse of the function f(x) = 2x + 1.

• f^(-1)(x) = 2x - 1

• f^(-1)(x) = (x - 1) / 2

• f^(-1)(x) = x + 1

• f^(-1)(x) = 2(x + 1)

9. What is the domain of the inverse function of f(x) = x^2 for x ≥ 0?

• (-∞, 0)

• (0, ∞)

• [0, ∞)

• [0, 1]

10. If f(x) = x + 2 and g(x) = 3x, what is (g ∘ f)(1)?

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