Mathematics 8 Quarter 2

• When the value of the variable y depends on the value of a variable x, then y is a dependent variable and x is an independent variable.
• A function is a rule that pairs each element in one set, called the domain, with exactly one element from the second set, called the range.
• Relations and Functions
• Every function is a relation, but not every relation is a function.
• The one-to-one and many-to-one relations satisfy the definition of a function.
• A one-to- many relation is NOT a function since a value of x is mapped more than one value.
• If a vertical line crosses the graph of a relation in more than one point, the relation cannot be a function.
• If no vertical line crosses the graph in no more than one point, then the graph is a graph of a function.
• A relation can be expressed using a table, mapping and graph.
• A relation is a rule that pairs each element in one set, called the domain with one or more elements from a second set called the range.
• The set of all first coordinates is the domain of the relation.
• The set of all second coordinates is the range of the relation.
• In listing the domain and the range, it should be in descending to ascending order.
• In case of having repeated value of either the range or the domain, write it once only.
• One-to-one correspondence Each value of x is mapped exactly to one value of y.
• Many-to-one correspondence Repeated value for y.
• One-to-many correspondence Repeated value for x.
• The one-to-one and many-to-one relations satisfy the definition of a function.