Variable
Content
Variable
A quantity that can change or that may take on different values. Variable
also refers to a letter or symbol representing such a quantity.
Independent Variable
A variable in an equation that may have its value freely chosen without
considering values of any other variable. For equations such as y = 3x – 2,
the independent variable is x. The variable y is not independent since it
depends on the number chosen for x.
Formally, an independent variable is a variable which can be assigned any
permissible value without any restriction imposed by any other variable.
Dependent Variable
A variable that depends on one or more other variables. For equations
such as y = 3x – 2, the dependent variable is y. The value of y depends on
the value chosen for x. Usually the dependent variable is isolated on one
side of an equation. Formally, a dependent variable is a variable in an
expression, equation, or function that has its value determined by the
choice of value(s) of other variable(s).
Expression
Any mathematical calculation or formula combining numbers and/or
variables using sums, differences, products, quotients (including
fractions), exponents, roots, logarithms, trig functions, parentheses,
brackets, functions, or other mathematical operations. Expressions may
not contain the equal sign (=) or any type of inequality.
Examples:
Formula
An expression used to calculate a desired result, such as a formula to find
volume or a formula to count combinations. Formulas can also be
equations involving numbers and/or variables, such as Euler's formula
Equation
A mathematical sentence built from expressions using one or more equal
signs (=).
Examples:
Relation
A set of ordered pairs.
For example, {(1, 2), (3, 4), (1, a), (5, r)} is a relation. So is the set {(x, y):
y = x2}; this is the set of all ordered pairs (x, y) for which y = x2.
Function
A relation for which each element of the domain corresponds to exactly
one element of the range. For example,
is a function because
each number x in the domain has only one possible square root. On the
other hand,
is not a function because there are two possible
values for any positive value of x.
Model
Mathematical Model
An equation or a system of equations representing real-world phenomena.
Models also represent patterns found in graphs and/or data. Usually
models are not exact matches the objects or behavior they represent. A
good model should capture the essential character of whatever is being
modeled.
A quantity that can change or that may take on different values. Variable
also refers to a letter or symbol representing such a quantity.
Independent Variable
A variable in an equation that may have its value freely chosen without
considering values of any other variable. For equations such as y = 3x – 2,
the independent variable is x. The variable y is not independent since it
depends on the number chosen for x.
Formally, an independent variable is a variable which can be assigned any
permissible value without any restriction imposed by any other variable.
Dependent Variable
A variable that depends on one or more other variables. For equations
such as y = 3x – 2, the dependent variable is y. The value of y depends on
the value chosen for x. Usually the dependent variable is isolated on one
side of an equation. Formally, a dependent variable is a variable in an
expression, equation, or function that has its value determined by the
choice of value(s) of other variable(s).
Expression
Any mathematical calculation or formula combining numbers and/or
variables using sums, differences, products, quotients (including
fractions), exponents, roots, logarithms, trig functions, parentheses,
brackets, functions, or other mathematical operations. Expressions may
not contain the equal sign (=) or any type of inequality.
Examples:
Formula
An expression used to calculate a desired result, such as a formula to find
volume or a formula to count combinations. Formulas can also be
equations involving numbers and/or variables, such as Euler's formula
Equation
A mathematical sentence built from expressions using one or more equal
signs (=).
Examples:
Relation
A set of ordered pairs.
For example, {(1, 2), (3, 4), (1, a), (5, r)} is a relation. So is the set {(x, y):
y = x2}; this is the set of all ordered pairs (x, y) for which y = x2.
Function
A relation for which each element of the domain corresponds to exactly
one element of the range. For example,
is a function because
each number x in the domain has only one possible square root. On the
other hand,
is not a function because there are two possible
values for any positive value of x.
Model
Mathematical Model
An equation or a system of equations representing real-world phenomena.
Models also represent patterns found in graphs and/or data. Usually
models are not exact matches the objects or behavior they represent. A
good model should capture the essential character of whatever is being
modeled.
