12 Questions
What is the domain of a relation?
The set of all input values
In the context of relations, what does the range represent?
The set of all output values
In the relation H = {(1, 72),(2, 64),(3, 60),(4, 57),(5, 71)}, what is the range?
{72, 64, 60, 57, 71}
What does the domain {x | x is a real number and x ≥ 0} represent?
Positive real numbers
In a graph where the domain extends from -8 to 8 and the range from -5 to 5, how would you express the range in set-builder notation?
{y | y is a real number and -5 ≤ y ≤ 5}
What does an open circle on a graph represent?
The graph excludes that point and ends there
What is an ordered pair?
A pair of numbers separated by a comma within parentheses
How are ordered pairs used in relations and functions?
To show a pairing of elements in a specific order
In the context of functions, what does the 'domain' refer to?
The set of input values
What is the purpose of deriving the inverse function of a given function?
To achieve symmetry in mathematical relationships
How are sets of ordered pairs related to relations or functions?
They can represent relations or functions
What distinguishes the pair (8, 5) from (5, 8) in mathematics?
(8, 5) has different ordering compared to (5, 8)
Study Notes
Relations and Functions
- A relation is a set of ordered pairs, where each pair consists of two elements, one coming first (input value or independent variable) and the other coming second (output value or dependent variable).
- The domain of a relation is the set of all first coordinates (input values), while the range is the set of all second coordinates (output values).
Ordered Pairs
- An ordered pair is a pair of numbers written within a set of parentheses and separated by a comma, such as (5, 8), where the order is designated by the first element (5) and the second element (8).
- The pair (8, 5) is not the same as (5, 8) due to the different ordering.
Examples of Relations
- The pairing of names and ages in a community is a relation, where each name is paired with a corresponding age.
- The pairing of student numbers and their corresponding heights is a relation, which can be written as a set of ordered pairs.
- The relation M = {(0, 0), (-6, 4), (1, 4), (-3, 4)} has a domain of {-6, -3, 0, 1} and a range of {0, 1, 4}.
Domain and Range Notation
- The domain and range can be expressed in set-builder notation or interval notation, such as {x | x is a real number and x ≥ 0} or [0, +∞) for the domain, and {y | y is any real number} or (-∞, +∞) for the range.
Graphical Representation
- Relations can be represented graphically in a rectangular coordinate system, where the domain consists of x-values and the range consists of y-values.
- The graph of a relation can help visualize the domain and range, such as the graph with a domain of [-8, 8] and a range of [-5, 5].
Test your understanding of relations and functions in Mathematics with this quiz based on Chapter I of the textbook 'Mathematics in the Modern World GEC 14 Teachers'. Explore how pairs of names and ages form ordered relations, and how to navigate between the two concepts effectively.
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