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# MATH AND TECHNOLOGY MATH 403

Texas A&M

GPA 3.6

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This 5 page Class Notes was uploaded by Vivien Bradtke V on Wednesday October 21, 2015. The Class Notes belongs to MATH 403 at Texas A&M University taught by Sandra Nite in Fall. Since its upload, it has received 18 views. For similar materials see /class/226017/math-403-texas-a-m-university in Mathematics (M) at Texas A&M University.

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Date Created: 10/21/15

Math 403 Lesson 3 Piece Functions Short Run and End Behavior and Transformations Piece Functions 3 xlt 1 Graph the function x2 1 s xS 2 2x 1 xgt2 Short Run and End Behavior 1 x 1 3 4 x322x 1 y x 10x 8 y x1x2x 8 5y x 42x5 x4 1 e 1nx7 239 y x 1x2 439 y x3 Find the following for the given functions a X and yintercepts f asymptotes b domain and range g 1imfxand lim fx 0 nvertibiity11 H f d maximumsminimums h39 900d V39ewmg W39ndow e intervals increasingdecreasing Transformations using Function Notation Graph y cos X Using function notation in the calculator graph the following a ycosx1 d ycosX2 g ycosx b ycosx 2 e y3cosx h ycosX c ycosX 1 f ycos3X i ycosx Graphy2x Using function notation in the calculator graph the following ay23 dy23 gy2X b y2quot 1 e y52quot h y2X c y2quot f y23x i y23939 Things to watch for on short run and end behavior of functions 0 xvalues where the function does not exist these will not be in the domain Examples include a zero in the denominator b negatives under an even root and 0 log ofa number less than or equal to zero 0 asymptotes and holes 0 places where the domain ends not asymptotes or holes what really happens there Trace closer and closer to find out 0 Functions that turn around close to the xaxis for roots not easily discernible Know your function zoom in close to the axis to see better 0 Maximums and minimums similar to the roots described above End behavior of functions that appear to have a horizontal asymptote in a relatively small viewing window Know the function zoom out to be sure 0 Horizontal asymptotes that are crossed Zoom in close enough to observe the behavior TEKS 2A l Foundations for functions The student uses properties and attributes of functions and applies functions to problem situations The student is expected to A identify the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous and discrete situations and 2A2 Foundations for functions The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations The student is expected to A use tools including factoring and properties of exponents to simplify expressions and to transform and solve equations an 2A10 Rational functions The student formulates equations and inequalities based on rational functions uses a variety of methods to solve them and analyzes the solutions in terms of the situation The student is expected to A use quotients of polynomials to describe the graphs of rational functions predict the effects of parameter changes describe limitations on the domains and ranges and examine asymptotic behavior B analyze various representations of rational functions with respect to problem situations C determine the reasonable domain and range values of rational functions as well as interpret and determine the reasonableness of solutions to rational equations and inequalities 2A 1 l Exponential and logarithmic functions The student formulates equations and inequalities based on exponential and logarithmic functions uses a variety of methods to solve them and analyzes the solutions in terms of the situation The student is expected to B use the parent functions to investigate describe and predict the effects of parameter changes on the graphs of exponential and logarithmic functions describe limitations on the domains and ranges and examine asymptotic behavior C determine the reasonable domain and range values of exponential and logarithmic functions as well as interpret and determine the reasonableness of solutions to exponential and logarithmic equations and inequalities P1 The student defines functions describes characteristics of functions and translates among verbal numerical graphical and symbolic representations of functions including polynomial rational power including radical exponential logarithmic trigonometric and piecewisedefined functions The student is expecte o A describe parent functions symbolically and graphically including fx X fx 1n X fx loga x fx lX fx ex fx IXI fx ax fx sin X fx arcsin x etc B determine the domain and range of functions using graphs tables and symbols D recognize and use connections among significant values of a function zeros maximum values minimum values etc points on the graph of a function and the symbolic representation of a function an E investigate the concepts of continuity end behavior asymptotes and limits and connect these characteristics to functions represented graphically and numerically Math 403 Lesson 4 Table Lists and Scatter Plots Table GRAPH Investigate the function fx 11 as X approaches in nity Use the trace and table x features of your calculator to investigate Describe what happens to the value of fX as X grows very large Use the calculator to give an estimate of e Using the table feature of the graphing calculator explore what integer value ofX rst gives the following estimates of e Estimate of e Table Start Value x 2 7 2T1 2718 27182 Lists and Scatter Plots STAT 2nd STAT 2nd Y The table below gives the number of domestic deaths from AIDS from 19811987 Make a scatter plot of the data Using a graphing calculator nd a linear function that ts the data Find an exponential function that ts the data Find a power function that ts the data Graph all three in the same viewing window Calculate the error sum of squares ESS for each Decide which functions best t the data Use each model to predict the total number of AIDS deaths in the US by the year 1998 when t 18 Discuss the variance in the three answers The table below continues the previous table Compare your answers to the actual recorded data below Make a scatter plot of the data through 1998 Does the power regression equation seem to fit this new data What seems to happen around 1996 Activities adapted from TEXTEAMS Algebra llPrecalculus Institute 612 Underlying processes and mathematical tools The student communicates about Grade 6 mathematics through informal and mathematical language representations and models The student is expected to A communicate mathematical ideas using language efficient tools appropriate units and graphical numerical physical or algebraic mathematical models 711 Probability and statistics The student understands that the way a set of data is displayed influences its interpretation The student is expected to B make inferences and convincing arguments based on an analysis of given or collected data 714 Underlying processes and mathematical tools The student communicates about Grade 7 mathematics through informal and mathematical language representations and models The student is expected to A communicate mathematical ideas using language efficient tools appropriate units and graphical numerical physical or algebraic mathematical models 815 Underlying processes and mathematical tools The student communicates about Grade 8 mathematics through informal and mathematical language representations and models The student is expected to A communicate mathematical ideas using language efficient tools appropriate units and graphical numerical physical or algebraic mathematical models A1 Foundations for functions The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways The student is expected to B gather and record data and use data sets to determine functional relationships between quantities C describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations D represent relationships among quantities using concrete models tables graphs diagrams verbal descriptions equations and inequalities and E interpret and make decisions predictions and critical judgments from functional relationships A2 Foundations for functions The student uses the properties and attributes of functions The student is expected to B identify mathematical domains and ranges and determine reasonable domain and range values for given situations both continuous and discrete C interpret situations in terms of given graphs or creates situations that fit given graphs and D collect and organize data make and interpret scatterplots including recognizing positive negative or no correlation for data approximating linear situations and model predict and make decisions and critical judgments in problem situations A5 Linear functions The student understands that linear functions can be represented in different ways and translates among their various representations The student is expected to A determine whether or not given situations can be represented by linear functions B determine the domain and range for linear functions in given situations and C use translate and make connections among algebraic tabular graphical or verbal descriptions of linear functions A11 Quadratic and other nonlinear functions The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations The student is expected to C analyze data and represent situations involving exponential growth and decay using concrete models tables graphs or algebraic methods 2A1 Foundations for functions The student uses properties and attributes of functions and applies functions to problem situations The student is expected to A identify the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous and discrete situations and B collect and organize data make and interpret scatterplots fit the graph of a function to the data interpret the results and proceed to model predict and make decisions and critical judgments P1 The student defines functions describes characteristics of functions and translates among verbal numerical graphical and symbolic representations of functions including polynomial rational power including radical exponential logarithmic trigonometric and piecewisedefined functions The student is expected to A describe parent functions symbolically and graphically including fx x fx 1n x fx loga x fx 1x fx ex fx x fx ax fx sin x fx arcsin x etc B determine the domain and range of functions using graphs tables and symbols D recognize and use connections among significant values of a function zeros maximum values minimum values etc points on the graph of a function and the symbolic representation of a function and E investigate the concepts of continuity end behavior asymptotes and limits and connect these characteristics to functions represented graphically and numerically P3 The student uses functions and their properties tools and technology to model and solve meaningful problems The student is expected to B use functions such as logarithmic exponential trigonometric polynomial etc to model reallife data C use regression to determine the appropriateness of a linear function to model reallife data including using technology to determine the correlation coefficient M1 The student uses a variety of strategies and approaches to solve both routine and nonroutine problems The student is expected to A compare and analyze various methods for solving a reallife problem B use multiple approaches algebraic graphical and geometric methods to solve problems from a variety of disciplines an C select a method to solve a problem defend the method and justify the reasonableness of the results M2 The student uses graphical and numerical techniques to study patterns and analyze data The student is expected to A interpret information from various graphs including line graphs bar graphs circle graphs histograms scatterplots line plots stem and leaf plots and box and whisker plots to draw conclusions from the data B analyze numerical data using measures of central tendency variability and correlation in order to make inferences C analyze graphs fromjournals newspapers and other sources to determine the validity of stated arguments and D use regression methods available through technology to describe various models for data such as linear quadratic exponential etc select the most appropriate model and use the model to interpret information

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