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Economics 214

Economics 214. Lecture 3 Introduction to Functions. Variables. Variables studied in economics can be qualitative or quantitative. Qualitative variable represents some distinguishing characteristic, such male or female, employed or unemployed.

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Economics 214

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  1. Economics 214 Lecture 3 Introduction to Functions

  2. Variables • Variables studied in economics can be qualitative or quantitative. • Qualitative variable represents some distinguishing characteristic, such male or female, employed or unemployed. • Quantitative variables can be measured numerically.

  3. Numbers • Integers are whole numbers. • Real numbers include all integers and all numbers between the integers. • Numbers that can be expressed as ratios of integers are call rational numbers. • Numbers that cannot be expressed as ratios of integers are call irrational numbers.

  4. Intervals • Interval is set of all real numbers between to endpoints. • Closed interval includes the endpoints. i.e. [1,2] • Open interval between two numbers excludes the endpoints. i.e. (1,2) • Half-closed or half-open interval between 2 numbers includes one endpoint and excludes the other endpoint. i.e. (1,2] • Infinite interval has negative infinity, positive infinity or both as endpoints. i.e. [0,∞)

  5. Sets • Set is simply a collection of items. • Item included in a set are called elements. • C={freshman,sophmore,junior,senior} • To show item is part of set we use symbol, . i.e. freshmanC • To show item is not part of set, we use symbol, . i.e. graduate studentC.

  6. Sets A set can be described either by listing all its elements or by describing the conditions required for membership. For Example N={10,20,30,40} Or N={x|x=10*y, y=1,2,3,4}

  7. Relations • The elements of one set can be associated with the elements of another set through a relationship. • A function is a relationship that has a rule that associates each element of one set with a single element of another set. • A function is also called a mapping or a transformation.

  8. Function • A function f that unambiguously associates with each element of a set X one element in the set Y is written as f:XY. • The set X is called the domain of the function f. • The set of values that occur is called the range of the function f.

  9. Example Function X={1,2,3,4} f:Y=10X Y={10,20,30,40} f:XY

  10. Univariate Function • A Univariate function maps one number, a member of the domain, to one and only one number, element of the range. • We represent the univariate function as y=f(x). • Y is the dependent variable or value of the function. • x is the independent variable or argument of the function.

  11. Examples of Univariate functions

  12. Ordered Pairs An Ordered pair is two numbers presented in parentheses and separated by a comma, where the first number represents the argument of the function and the second number represents the corresponding value of the function. Each ordered pair for the function y=f(x) takes the form (x,y).

  13. Example of Ordered Pair

  14. Graphing • Ordered pairs can be plotted in a Cartesian plane. • The origin of the plane occurs at the intersection of the two axes that are a right angles to each other. • Points along the horizontal axis represent values of the argument of the function.

  15. Graphing Continued • Points along the vertical axis represent values of the function. • The coordinates of a point are the values of its ordered pair and represent the address of that point in the plane. • The x-coordinate of the pair (x,y) is called the abscissa, and the y-coordinate is called the ordinate. • The origin is represented by the ordered pair (0,0).

  16. Plot of our function

  17. Graph • Graph of a function represents all points whose coordinates are ordered pairs of the function.

  18. Graph of our function

  19. Linear function

  20. Graph Linear Function

  21. Graph function in multiple quadrants

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