# Functional relationship between variables

### Functional Relationship Examples: Distance-Time Graphs and Temperature-Precipitation Graphs

A real-life example of a functional relationship is the relationship between of functional relationships helps us figure out how different variables work together. Functional relationships. • We frequently need to represent economic quantities as a mathematical function of one or more variables, e.g.: • A firm's costs as a. Determining if a Relationship is a Functional Relationship To determine whether or not a graph is a function, you can use the vertical line test. . A function exists when each x-value (input, independent variable) is paired with exactly one.

The following are examples of monomials: Polynomial comes from the Greek word, poly, which means many. A polynomial has two or more terms i. If there are only two terms in the polynomial, the polynomial is called a binomial. These terms are 4x3y2, - 2xy2, and 3. The coefficients of the terms are 4, -2, and 3. The degree of a term or monomial is the sum of the exponents of the variables. The degree of a polynomial is the degree of the term of highest degree.

In the above example the degrees of the terms are 5, 3, and 0. The degree of the polynomial is 5. Remember that variables are items which can assume different values.

## Variables, Functions and Equations

A function tries to explain one variable in terms of another. Consider the above example where the amount you choose to spend depends on your salary. Here there are two variables: Independent variables are those which do not depend on other variables. Dependent variables are those which are changed by the independent variables. The change is caused by the independent variable. In our example salary is the independent variable and the amount you spend is the dependent variable.

**13-1 Relationships Between Variables**

To continue with the same example what if the amount you choose to spend depends not only on your salary but also on the income you receive from investments in the stock market. Now there are three variables: A function is a mathematical relationship in which the values of a single dependent variable are determined by the values of one or more independent variables. Function means the dependent variable is determined by the independent variable s. A goal of economic analysis is to determine the independent variable s which explain certain dependent variables.

For example what explains changes in employment, in consumer spending, in business investment etc.? Functions with a single independent variable are called univariate functions.

There is a one to one correspondence.

Functions with more than one independent variable are called multivariate functions. The independent variable is often designated by x. The dependent variable is often designated by y. We say y is a function of x. This means y depends on or is determined by x. If we know the value of x, then we can find the value of y.

In pronunciation we say " y is f of x. In other words the parenthesis does not mean that f is multiplied by x. It is not necessary to use the letter f.

We may look at functions algebraically or graphically. If we use algebra we look at equations. If we use geometry we use graphs.

In other words a variable is something whose magnitude can change. It assumes different values at different times or places. Variables that are used in economics are income, expenditure, saving, interest, profit, investment, consumption, imports, exports, cost and so on.

It is represented by a symbol. Variables can be endogenous and exogenous. An endogenous variable is a variable that is explained within a theory. An exogenous variable influences endogenous variables, but the exogenous variable itself is determined by factors outside the theory.

### Basic Tools in Economic Analysis - WikiEducator

Ceteris Paribus is an assumption which we are compelled to make due to complexities in the reality. It is necessary for the sake of convenience. The limitations of human intelligence and capacity compel us to make this assumption.

Besides, without the assumption we cannot reach on economic relations, sequences and conclusions. In fact, there are large number of variables interacting simultaneously at a given time. If our analysis has to be accurate we may have to examine two variables at a time which makes it inevitable to assume other variables to remain unchanged.

For instance, if we try to establish the relationship between demand and price, there may be other variables which may also influence demand besides price. The influence of other factors may invalidate the hypothesis that quantity demanded of a commodity is inversely related to its price. If rise in price takes place along with an increasing in income or a change technology, then the effect of price change may not be the same.

However, we try to eliminate the interrupting influences of other variables by assuming them to remain unchanged. The assumption of Ceteris Paribus thus eliminates the influence of other factors which may get in the way of establishing a scientific statement regarding the behavior of economic variables.

A simple technical term is used to analyze and symbolizes a relationship between variables. It is called a function. It indicates how the value of dependent variable depends on the value of independent or other variables. It also explains how the value of one variable can be found by specifying the value of other variable. For instance, economist generally links demand for good depends upon its price. Functions are classifieds into two type namely explicit function and implicit function.

Explicit function is one in which the value of one variable depends on the other in a definite form. For instance, the relationships between demand and price Implicit function is one in which the variables are interdependent.

## Functional relations between variables

When the verbal expressions are transformed into algebraic form we get Equations. The term equation is a statement of equality of two expressions or variables.

The two expressions of an equation are called the sides of the equation. Equations are used to calculate the value of an unknown variable. An equation specifies the relationship between the dependent and independent variables.

### secondary mathematics functional relations between variables | Nuffield Foundation

Each equation is a concise statement of a particular relation. For example, the functional relationship between consumption C and income Y can take different forms. It says nothing about the form that this relation takes.