Exploring Relations and Functions

What is the definition of a relation in mathematics?

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

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

• A relation is a collection of unordered elements from one set.

• A relation is a mathematical function that maps elements to real numbers.

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

• Yes, the set is a function.

• The set contains unique pairs only.

• The set has more than one output for an input.

• No, the set is not a function.

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

• 9

• 14

• 7

• 11

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

• (-∞, 5) ∪ (5, ∞)

• (-∞, 5]

• (5, ∞)

• [5, ∞)

What is the range of the function f(x) = x^2 for all real numbers?

• (-∞, 0)

• [0, ∞)

• (0, 1)

• [1, 2]

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

• No, it is not a function because it has duplicate inputs.

• Yes, it is a function but it is not defined for all integers.

• Yes, it is a function.

• No, it is not a function because the output is not unique.

If f(x) = 3x - 1, what is f(4)?

• 12

• 11

• 10

• 9

Determine the domain of the function f(x) = √(x - 2).

• [1, 2)

• (2, ∞)

• (-∞, 2)

• [2, ∞)

Evaluate (g ∘ f)(x) if f(x) = x + 1 and g(x) = 2x. What is (g ∘ f)(3)?

• 8

• 4

• 10

• 6

What is the range of the function f(x) = -x^2 + 4?

• (-∞, 4]

• (4, ∞)

• (-∞, 0]

• [0, 4]