# function - ECON1003 Mathematics for the Social Sciences...

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ECON1003 Mathematics for the Social Sciences Topic 1: Functions Lecturer: Marlon Tracey

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Objective o At the end of this topic, students should be able to: o Define and identify a function o Distinguish among types of functions o Derive composite and inverse functions o Apply functions to real world situations o Apply the remainder and the factor theorem o Sketch and transform graphs of functions
Outline 1. Definition of a function 2. Evaluating a function 3. Domain and range of functions 4. Identifying a function 5. Categorizing functions 6. Composite functions 7. Inverse functions 8. Special functions 9. Applications of functions 10. Remainder theorem, factor theorem and solving cubic equations. 11. Sketching graphs of functions 12. Transforming graphs

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Relevance o Functions are widely used to mathematically describe the relationship between variables. o Indeed, if one’s years of experience is related in some way” to one’s salary, then years of experience can be used to predict salary.
Defining a function I o Example 1.1: Let X ={1, 2, 3} and Y = {2, 4, 6}. o Each member of set Y is two times its corresponding member of set X. o That is to say, y = 2x o A function is a mathematical rule which associates every member of a set X with exactly one member from a set Y .

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Defining a function II o Y is usually written as f (X), which means “a function of X”. That is, X determines what Y is through the function f [ which is the same thing as saying x maps to y through f , that is, f: X → Y ] o If a worker is paid by the hour, his weekly pay is a function of how many hours he worked. That is, pay = f(hours) o A function can be written as an equation, such as y = 2x. o Or as an ordered pair where every member of X is paired with exactly one member from Y, such as {(1,2), (2,4), (3,6)}. Note the first value comes from X and the second comes from Y. o Or displayed in the form of a graph, diagram etc.
Defining function III: Equation form Examples: o F1: o F2: y = 3x +1 o F3: y = (x + 2) 3 o F4: y= -x 2 o F5: o F6: o F7: y = log(x) 3 1 ) ( - = x x f

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Defining a function IV: Diagram form 1 2 3 4 5 6 7 8 9 10 Bob Joe Ted Ron Peter 18 19 20 22 24
Defining a function V: Graphical form

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Evaluating a function o Evaluating a function at a particular value means to replace x (or whatever the variable is) with the value. o For example, evaluating the function f(x) = 2 x - 5 at x = 6 means to substitute 6 where x is as follows: f ( 6 ) = 2 ( 6 ) - 5 = 7. o Therefore, f ( 6 ) = 7. The quantity inside the parentheses is x and the quantity on the right of the equal sign (the result) is y . o Exercise : Evaluate all the functions on slide 6 at x = 3.
o The set X is called the domain of the function f , and the set Y contains the range . o

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## This note was uploaded on 03/16/2011 for the course ECON 1003 taught by Professor Dr.mcdonald during the Spring '11 term at University of the West Indies at Mona.

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function - ECON1003 Mathematics for the Social Sciences...

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