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# Stat,Functns,& Rates of Chng MATH 135

WCU

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This 14 page Class Notes was uploaded by Alphonso Thompson on Thursday October 29, 2015. The Class Notes belongs to MATH 135 at Western Carolina University taught by Staff in Fall. Since its upload, it has received 16 views. For similar materials see /class/230965/math-135-western-carolina-university in Mathematics (M) at Western Carolina University.

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Date Created: 10/29/15

MATH 135 Statistics Functions and Rates of Change Contents 1 Lecture Notes 4 11 Selected terms from Chapters 1 and 2 4 12 Functions 6 13 Function notation 10 14 Linear functions7 part 1 12 15 Linear functions7 part 2 15 16 Distributive property and factoring review 21 17 Percentages a quick review 23 18 Exponents and exponential growth 25 19 Simplifying rational expressions 30 110 lnformal introduction to limits 31 111 Average rate of change 34 112 Instantaneous rate of change the derivative 37 113 Derivatives7 part 2 40 114 An application of derivatives to economics 44 2 Homework Exercises Probability and Statistics 48 21 Venn diagrams 48 22 Probability problems deck of cards 50 23 Probability problems pair of dice 52 24 Contingency tables7 part 1 54 25 Contingency tables7 part 2 57 26 Multiplication rule for independent events 59 27 Extra problems on the normal distribution7 part 1 61 28 Extra problems on the normal distribution7 part 2 62 3 Homework Exercises 63 a 31 Brush up on your equation solving skills 63 32 Functions 64 33 Function notation 67 34 Linear functions part 1 69 35 Linear functions part 2 71 36 Distributive property and factoring review 74 37 Percentages a quick review 75 38 Exponents and exponential growth 76 39 Simplifying rational expressions 78 310 lnforrnal introduction to lirnits 79 311 Average rate of change 80 312 lnstantaneous rate of change the derivative 81 313 Derivatives part 2 82 Selected answers 84 41 Venn diagrarns 84 42 Probability problerns deck of cards 85 43 Probability problerns pair of dice 86 44 Contingency tables part 1 87 45 Contingency tables part 2 88 46 Multiplication rule for independent events 89 47 Extra problems on the normal distribution part 1 90 48 Brush up on your equation solving skills 91 49 Functions 92 410 Function notation 93 411 Linear functions part 1 94 412 Linear functions part 2 95 413 Distributive property and factoring review 96 414 Percentages a quick review 97 415 Exponents and exponential growth 98 416 Sirnplifying rational expressions 99 417 lnforrnal introduction to lirnits 100 418 Average rate of Change 419 Instantaneous rate of Change the derivative 420 Derivatives7 part 2 101 1 Lecture Notes 11 Selected terms from Chapters 1 and 2 a numerical facts b a discipline of study methods used to collect analyze present and interpret data and to make decisions and inferences based upon that data Population Element or Member of the population Sample biased sample representative sample random sample strati ed sample Variable categorical qualitative numeric quantitative discrete continuous Descriptive vs lnferential statistics Some methods of displaying data frequency distribution pie Chart bar graphhistogram stem and leaf display boxplot box and whisker plot Some shapes of distributions unimodal bimodal symmetric positively or negatively skewed Outlier 12 Functions Function Domain Range May be expressed many ways7 such as pictorially7 as tables7 as ordered pairs7 or graphically Example of a function expressed several ways Domain Range Many functions can be expressed by an equation Example of an equation7 a partial table of values7 and its graph Examples of relationships which are NOT functions The vertical line test Sample problems 1 Consider the set of ordered pairs 1 1 2 2 3 3 4 4 5 5 a Make a graph of the points on the X y plane b ls this a function c What is the domain the range 2 By plotting several points and connecting them with a reasonable curve sketch a graph of the function de ned by the equation y X2 a Verify using the vertical line test that this is a function b What is the domain the range 3 Sally and Samantha live on the same oor of their residence hall Their rooms are 50 feet apart Walking at a constant rate7 Sally walks from her room to Sarnantha7s room in 15 seconds a Make a graph representing Sally7s distance from her room as a function of time b Make a graph representing Sally7s distance from Sarnantha7s room as a function of time 13 Function notation Shorthand notation for y is a function of X y f f77 is read the f of x o z is the input variable usually called the independen 77 variable 0 y is the output variable usually called the dependent77 or the response77 variable Examples f 2x 4 f3 f 10 996 962 7 1 92 90 Piecewise de ned function 2x M96 2 h72 h3 Make a sketch of the function f 2x f0 f 8 974 92 if x S 0 if z gt 0 h0 1 if z lt 0 Make a sketch of the function f 2s if20 For the function whose graph is shown at the right7 the domain is the range is f0 and M f 4 ll in the blank 14 Linear functions part 1 Determine the next 2 values in each of the following tables Then explain the pattern that you see in the numbers X y x y X y 0 3 0 3 0 0 1 6 1 7 1 1 2 9 2 11 2 4 3 12 3 15 3 9 4 15 4 19 4 16 5 5 5 6 6 6 The rst two tables but not the third represent linear data A linear function is a function whose graph is a line Recognizing linear data from a table like above Note the pattern in the second table f03 f134 f2344324 f33444334 f434444344etc ln general7 a linear function can be written in the form f b 77w or y b mm This is known as the slope intercept form of a line the y intercept b is the slope m is Write linear equations which model the data in the rst 2 tables above and sketch their graphs Give a graphical interpretation of the slope and y intercept in each case Given any two points 1 yl and 2 yg on the graph of a linear function yZ 7 11 Mi 2 7 1 run39 the slope m This is frequently called Verify that the slope is constant regardless of the 2 points chosen in the examples above A line goes through the points 0 2 and 3 11 Sketch the line nd its slope and write an equation of the line in y b ms forrn

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