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# Math M119 Ch 1 Sec 1 and 2 Notes M119

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## Popular in Brief Survey of Calculus

## Popular in Mathematics (M)

This 10 page Bundle was uploaded by Meegan Voss on Monday January 25, 2016. The Bundle belongs to M119 at Indiana University taught by Gregory Kattner in Winter 2016. Since its upload, it has received 39 views. For similar materials see Brief Survey of Calculus in Mathematics (M) at Indiana University.

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Date Created: 01/25/16

Chapter 1 Section 1 What is a Function Let A a b c and B p q r represent two sets If we describe a correspondence between the member of A and those of B in which each member of A is matched up with one and only one member of B then we have described a function We refer to A as the domain set The members of B that are matched up with members of A form what we refer to as the range set of the function We also refer to the members of the domain as the inputs for the function and the members of B as the outputs or as the values of the function The set of members in the codomain that have been matched up with some members from the domain forms the set that we call the range of the function The range set is always a subset of the codomain It is the correspondence itself that is the function Ex Let A a b c and B p q r represent two sets The following correspondence is a function Let a correspond to q Let b correspond to q Let c correspond to p Ex The following correspondence is not a function Let a correspond to q Let b correspond to q and also to p Let c correspond to r Ex The following correspondence is not a function Let b correspond to r Let c correspond to q Ex The following correspondence is a not function Let A be the set of positive integers let B be the set of positive integers let x represent some member from A and let 2x 7 represent the number that x is to correspond to Ex The following correspondence is a function Let A be the set of real numbers let B be the set of real numbers let x represent some member from A and let 5x3 represent the number that x is to correspond with The functions that we study will mostly all have the set of real numbers as the domain set and a subset of the real numbers as the range set Let x be some real number and let lm represent the number that x is to correspond with If we choose to name this function as f then we can present our function by writing the equation fxm A function can be described by giving an equation as in fxm A function can be I O described by giving a h 5 1 3 9 table of its values I The values hit decrease as r increases We call hlt an decreasing function A function can be described by displaying its values in a graph A graph of the function rt appears on the next page What is r70 Find a value of t for which rt 50 This is an example of an increasing function EU lam in ad El Elli QHEH Chapter 1 Sectien 21 Linear Functions A linear function is one which can be described by an equation of the form fx mx b The number m is called the slope and b is called the vertical intercept When the values of a linear function are displayed in a rectangular coordinate system that has a linear scale on each axis then the graph appears as a line The function fx 2x 5 appears in the graph below LII Review of basic concepts Write the equation of the line whose graph passes through the points 25 and 37 The answer is y fx O4x 58 l l l ll a a am Using the table below express p as a linear function of q Next express q as a linear function of p The answers are p fq O5q 35 and q gp 2p 7 The words quotexpress p as a linear function of q tell us to consider q as the input variable Usually we think of x as the input variable but sometimes other letters are used in a problem so you will need to pay attention to the wording of the problem so that you know how to proceed Note that a linear function has a constant rate of increase that is to say the line has a constant slope You can see this in the table above by noting that every time p increases by 2 the value of q then decreases by 4 As time permits Consider question 17 on page 13 of the text book Which of the three tables could describe a linear funcUon Often times there are units of measure that are associated with the input and the output variables of a function These are important to keep in mind when analyzing a function and its values Consider questions 15 and 22 in the text book on pages 13 and 14 respectively 22A P Pt 40415t 1241 z 269t 1241 228 The slope has units of quotmillions of tons per yearquot 22C The vertical intercept is when t O the year is 1975 and at that time production was 1241 tons 22D t 40 in the year 2015 P40 z 2317 tons 22E Find t so that Pt 2500you nd that t z 468 When 468 years have passed the calendar will read 2021 Note that we re considering t as the number of years since the start of 1975

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