Exploring Relations and Functions

What is the definition of a relation in mathematics?

• A relation is a single pair of elements from two sets.

• A relation is a function that maps elements from one set to another.

• A relation is a set of ordered pairs that defines a relationship between elements of two sets.

• A relation is a collection of unordered elements from multiple sets.

Identify whether the set {(1, 2), (2, 3), (3, 4)} is a function.

• Yes, it is a function.

• No, it is not a function.

• It is a function but not defined properly.

• It is a function with multiple outputs.

Evaluate the function f(x) = 2x + 3 for x = 5.

• 10

• 15

• 8

• 13

What is the domain of the function f(x) = 1/(x - 2)?

• All real numbers

• x < 2 or x > 2

• All real numbers except x = 2

• x = 2 only

Determine the range of the function f(x) = x^2.

• [1, 2]

• [0, ∞)

• (0, 1)

• (-∞, 0)

Is the relation {(1, 2), (1, 3), (2, 4)} a function? Why or why not?

• No, it is a function because it has multiple outputs for one input.

• Yes, it is a function since there are no repeated inputs.

• Yes, it is a function because each input has a unique output.

• No, it is not a function.

Find f(0) if f(x) = 3x^2 - 2x + 1.

• -1

• 0

• 1

• 2

What is the domain of the function f(x) = √(x - 1)?

• [0, 1]

• (-∞, 1)

• (1, 2)

• [1, ∞)

Evaluate f(-2) for the function f(x) = x^2 + 4x + 4.

• 0

• -4

• 8

• 4

Determine the range of the function f(x) = -x + 5.

• Only positive numbers

• All real numbers

• Only negative numbers

• Numbers between 0 and 5