Understanding Relations and Functions

What is the definition of a relation in mathematics?

• A relation is a collection of unordered elements without any specific pairing.

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

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

• A relation is a function that maps every element of one set to a unique element of another set.

How can you determine if a relation is a function?

• A relation is a function if each input has exactly one output.

• A relation is a function if it has multiple outputs for the same input.

• A relation is a function if it includes at least one input-output pair.

• A relation is a function if it is represented by a straight line on a graph.

Given the set of ordered pairs {(1, 2), (2, 3), (1, 4)}, is this relation a function? Why or why not?

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

• No, this relation is not a function.

• This relation is a function since it has only one output for each input.

• Yes, this relation is a function because all inputs are unique.

Identify the domain of the function f(x) = 2x + 3.

• Only positive numbers

• Only negative numbers

• Integers between 1 and 10

• All real numbers

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

• (-∞, 0)

• [0, ∞)

• (0, 1)

• [1, 2]

What is the domain of the relation represented by the set of points {(3, 5), (4, 6), (5, 7)}?

• {2, 4, 5}

• {3, 4, 5}

• {3, 4, 6}

• {1, 2, 3, 4, 5}

If a function is defined as f(x) = 1/(x-2), what is the domain?

• All real numbers

• All real numbers except x = 2

• x < 2

• x = 2 only

Explain how to find the range of the function f(x) = -x^2 + 4.

• (-∞, 4]

• (4, ∞)

• [0, 4]

• (-∞, 0)

Given the function g(x) = √(x-1), what is the domain?

• (−∞, 1)

• (1, 2)

• [0, 1]

• [1, ∞)

Is the relation defined by the equation y = 2x + 1 a function? Explain your reasoning.

• No, it is a function but it has no real solutions.

• Yes, it is a function but only for positive values of x.

• No, it is not a function because it does not pass the vertical line test.

• Yes, it is a function.