Get Chegg Math Solver. The one-to-one property of logarithmic functions tells us that, for any real numbers x > 0, S > 0, T > 0 and any positive real number b, where b 1, log b S = log b T if and only if S = T. For example, If log 2 ( x 1) = log 2 ( 8), then x . It includes graphing linear, absolute value, quadratic, cubic, quartic, radical, exponent. This page will be removed in future. htRMhA~'HRTk`a[(I4iJs? We have a new and improved read on this topic. A quadratic function has a slope that changes signs at the vertex (and a constant, nonzero second derivative). It is denoted by g (x) = log e x = ln x. ;VWr}_ G{N A graph is a visual method of illustrating the behaviour of a particular function. b>1 b > 1. the function grows in a manner that is proportional to its original value. I thought it would be great review to mix up all of the functions we had discussed so that they had to determine how to go about graphing the specific type of function. For a formal introductory definition on the topic, it's an algebraic equation which is solved in just one step, that's why it's called so. This escape room (digital breakout) activity was created using Google Slides. Worksheets are Quadratic exponential and logarithmic functions, Algebra ii exponential regression work value 10, Math 130 problems linear quadratic and exponential functions, Work 2 7 logarithms and exponentials, Function family fun, Building exponential logarithmic and logistic models, Model fitting with . - Coefficient of determination, standard error of the estimate, standard error of the slope, t and F statistics The first is the shape of an exponential function. There are three activities within the escape room which include matching, multiple-choice, and interactive slide questions. 1, MSA KENYA. (Linear, quadratic, cubic, or exponential) An exponential function. The main property that we'll need for these equations is, logbbx = x log b b x = x. Sound Broadcasters use a parabolic microphone on football sidelines to pick up field audio for broadcasting purposes. Linear Inequalities in Two Variables. This Purchase includes:9 FUNCTION FAMILIES NOTE GUIDE: Students will use this note guide to create the graphs of the 9 Basic Function Families using the Parent Function Rule. Quadratic Function. If log x = log y, then x = y. Displaying all worksheets related to - Quadratic Logarithmic And Exponential Regression. Exp is the inverse function of the. Graphing Exponential Functions Calculator. $$. If f (z) is a quadratic function, then the corresponding directional and quadratic selection gradients, again if the relevant aspect of fitness is the number of intervals survived, can be obtained using equations . - Application of simulation models, NYERERE AVE, MAGANJO BLDG, 2ND FLOOR SUITE NO. Since, the exponential function is one-to-one and onto R+, a function g can be defined from the set of positive real numbers into the set of real numbers given by g (y) = x, if and only if, y=e x. R`:>;qpr7\62qr+E{YmiJ%zHloirg|&'. - Models - additive and multiplicative models Determine the relationship shown in the table with the correct reasoning. A quadratic function is graphed as a parabola, changes the sign of its slope at the vertex, and has differences that increase by a constant amount in each time interval. This set includes 12 cards with tables. - Monte Carlo simulation Intended for students needing to prepare for calculus. - Assumptions of linear regression analysis - Transportation and assignment problems, - Decision making process To solve an exponential equation, the following property is sometimes helpful: If a > 0, a 1, and a x = a y, then x = y. Linear Functions and Their Graphs. This is a multi-day project that will connect the real world to linear, quadratic, and exponential functions. Standards Textbook. - Analysis of Variances (ANOVA), - Definition of time series Answer: They all refer to how long it takes to run a computer program with large inputs, and specifically how much longer it takes with larger inputs. However, its range is such that y R. Remember that logarithmic functions and exponential functions are inverse functions, so as expected, the domain of an exponential is such that x R, but the range will be greater than 0. Question 5: Solve. TI-84 Plus Silver Edition. a is y-intercept or the value of y when x = 0, b is the slope or gradient or the amount by which y changes in value when x changes by a unit, Properties/characteristics of linear functions. polar coordinates (r,)?. - Resource scheduling (leveling) and Gantt charts Represent exponential and logarithmic functions that model real-world situations using graphing technology and describe their inverse relationship. Learn how to distinguish between linear, exponential, and quadratic models. Solution for For each function, state whether it is linear, quadratic, or exponential. Mzd[Ls23cs9zvW9=9>}~3h?oseOQv yop 8 = 2x 10 Apply the one-to-one property of exponents. There are 56 graph cards with graphs students should recognize in a moment. D. 6. exponential linear quadratic logarithmic 2 See answers Just passing the answer Advertisement Advertisement s136987 s136987 2022 EDGE ASSIGNMENT . For each function, they are also asked to identify several characteristics, such as: function family transformations domain and range end behaviorincreasing/decreasing intervals asymptotesy-interceptThis is a great review activity for Algebra 2/Pre-Calc students. Parent Functions And Their Graphs (solutions, Examples, Videos, Worksheets, Games, Activities) www.onlinemathlearning.com. Linear. ~I personally used this activity in my Algebra 2 class to prepare for the California State Test (CAASPP or SBAC). 5. - Differentiation of exponential and logarithmic functions $$ $$ First Version: Self Correcting Maze Where students type in the answersSecond Version: Self Correcting Maze with drop down menu w, This is a 16 question worksheet on graphing most types of functions covered in Algebra 2. 10th - 11th grade . - Pure strategy games (saddle point) f (x) = 2x + 12. Note: In a given analysis there are two types of variables namely: A function is a mathematical expression which describes a relationship between two or more variables in a particular analysis specifically one dependant variable and one or more independent variables. Great for bulletin boards! (a) Use the regression feature of a graphing utility to find a linear model, a logarithmic model, a quadratic model, an exponential model, and a power model for the data. {"6'IDMy{ M7 ' > ["srzf#0CG[z#Yx0o@T[d, 5URBqM!,-k09I`UT%Y3"b,6I+YDT#! y=b^x y = bx. (B)(-r,+2) Suppose you go to a track meet to watch your friends Beth, Marla, and Tracy compete in a 5K race. This is very common with exponential functions especially with population and growth . Every quadratic function has a "u-shaped" graph called a parabola. What type of function is represented in the table? To better organize out content, we have unpublished this concept. )IV & \ Y ( - 2 , - \pi / 3 ) Students will also match each function to its graph. - Sensitivity analysis and economic meaning of shadow prices in business situations The digital version is self grading m, This Algebra - PreCalculus Graph Cards Graphs your students NEED to know resource with both Matching and Sorting Activities makes a great back to school resource.Included are two sets of cards.Study cards - This resource is designed for Algebra 1, Algebra 2, Trigonometry, and PreCalculus. Add highlights, virtual manipulatives, and more. The first difference of the y values in the table is the same. . - T-ratios and confidence interval of the coefficients Parent Functions and Transformations Reference BookThis reference book was created to use as a review of transformations and the following function families: linear, absolute value, quadratic, cubic, square root, cube root, exponential, logarithmic, and reciprocal Students will graph the both the parent function and a transformation graph for each function family. Write linear, quadratic, and exponential functions Algebra 1 Math Worksheets. Videos Lesson 7.6 Modeling Data_ Exponential Logarithmic and Quadratic Functions.docx. These no-prep resources include 6 lessons with guided notes, an exi, Get a complete, ready-to-print unit covering topics from the Algebra 2 TEKS including domain and range, function families and parent functions, inverse relations, and inverse functions. Each has Organizers and Interactive Notebook pages.Some have templates included. November 6, 2022 by ppt. Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter? Log in. In this digital maze students will naming function families based on a given equation, graph or description of the degree of the function. Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials. - Project evaluation and review technique (PERT) y = abx Write the general form of an exponential function. Solve. z* j .V I+ 5 P'+M6uHYP? Use the graphs to choose the model that you think best fits the data. The function families included in this activity are: Linear, Quadratic, Cubic, Absolute Value, Reciprocal, Rational, Logarithmic Exponential and Radical. After setting up the appropriate inequality, we have, Therefore the domain of the function is the interval . 90 0 obj <> endobj For example by looking at a graph we can tell whether f(x) is increasing or decreasing as x increases or decreases. - Elementary single server queuing systems Introduction to Functions Unit, Algebra 2, Introduction to 9 Function Families Note Guide & Scavenger Hunt Extension, UNIT NOTE GUIDE BUNDLE! 7. Introduction to Functions Unit, Algebra 2, Also included in:UNIT NOTE GUIDE BUNDLE! Planning the Solution What is the equation for a vertical parabola with vertex at the origin? Introduction to Functions | Algebra 2, Parent Functions and Transformations - DIGITAL pixels activity, Function Transformations Independent Practice Book and Guided Instruction Format, Graphing Bundle - 52 Walk Around Activities~Linear~Quadratic~Inequalities, Graphing Functions & Finding Characteristics. 0. - Expected value, variance, standard deviation and coefficient of variation using frequency and probability, - Discrete and continuous probability distributions (uniform, normal, binomial, poisson and exponential) exponential function. Algebra 2 Scavenger Hunt and Activity Bundle, Writing Functions w/Transformations -Linear, Quadratic, Exponential, Logarithmic, Writing Functions w/Transformations: Linear, Quadratic, Exponential, Logarithmic, Foundations for Functions - Unit 1 Bundle - Texas Algebra 2 Curriculum, Foundations for Functions - Unit 1 - Texas Algebra 2 Curriculum, Graphing Piecewise Functions Self Grading Digital Assignment plus PRINTABLE, PreCalculus Unit 1 Functions & Graphs Digital Bundle plus Print, Graphs Your Students MUST KNOW Matching for Algebra PreCalculus, Functions Graphs and Key Properties Digital Bundle plus Print, Functions and Transformations Review | Digital Escape Room | Breakout, Functions and Transformations | Digital Interactive Notebook BUNDLE. View complete answer on khanacademy.org What are the 8 key features of a function? On a graph, a quadratic function is a . $$ Random Posts. Step 2 Write the function. This is an expanding bundle! - Partial derivatives and their applications 28 = 22x 10 Use the one-to-one property of exponents. This unit lays the groundwork for a strong foundation in topics that reemerge throughout Algebra 2. alternatives . That is, use. = Exponential utility function, where a>0; log_eut R ,x E ln R ,x(( )) = (( )) % % = Logarithmic utility function. - Venn diagrams, - Definitions: event, outcome, experiment, sample space Oops, looks like cookies are disabled on your browser. There is a constant ratio of 7. FUNCTIONS Definitions Variables A variable is any quantity that assumes different values in a particular analysis. and also 9.7: Linear, Quadratic, and Exponential . $$ Maximum and minimum values of the function can be seen at a glance. Rearrange if necessary. Use solutions to linear, quadratic, exponential and logarithmic equations to determine market equilibrium price and quantity. Learn how to distinguish between linear, exponential, and quadratic models. f (x)=5x-10. Linear functions are graphed as straight lines while exponential functions are . Create the scene for your students to discover the effects of the a, h, and k values on the graphs of Parent Functions using this 3-day investigation of the crimes / transformations of the Cryptic K (translations up & down), Elusive H (translations left & right), and Illicit A (reflections, Introduce your students to 9 Function Families (Linear, Quadratic, Cubic, Absolute Value, Square Root, Exponential, Logarithmic, Rational, Sine), the key features of their function rules, and the key features of their graphs using this Introduction to the 9 Function Families Note Guide & Scavenger Hunt Extension. Examples are: Production costs Material costs Sales revenue Constant This is any quantity whose value remains unchanged in a particular analysis Examples ar Fixed costs Rents Tuition fees: Note: In a given analysis there are two types of variables Functions, equations and . x = 9 Divide by 2. This is a lesson worksheet for direct instruction on writing functions from the transformations on a graph. How much will it cost you to mail 400 surveys. Fill-in-the-blank vocabulary im, Parent Functions Linear Quadratic Exponential Logarithmic Graphs, Functions and Their Graphs (PreCalculus Unit 2) | All Things Algebra, PreCalculus Curriculum | All Things Algebra, Parent Functions & Transformations Reference Book, GOOGLE FORMS Algebra 1 Parent Functions and Transformations Practice, BACK TO SCHOOL | Algebra 1 Curriculum DIGITAL ALL INCLUSIVE Resource Membership, Graphing Functions Stained Glass Art Bundle, Transformations of 9 Function Families (a, h, and k) Investigation Activity, FULL UNIT BUNDLE! - Non zero sum games Polynomial Functions . Then give two other polar coordinate representations of the point, one with r < 0 and the other with r > 0. Function 1 X 0 1 2 3 4 Quinear y -3 -12 -3 24 69 Function 2 X 1 2 3 4 5 Enter your Pre Calculus problem below to get step by step solutions. We will also discuss what many people consider to be the exponential function, f (x) =ex f ( x) = e x. Logarithm Functions - In this section we will introduce logarithm functions. An exponential function. functions graphs linear quadratic exponential function graph equations graphing examples biv type math chapter modeling algebra comparison extra help determine. The gun goes off and you watch each of your friends run . `exp(x^2-4)=4`, solver shows the calculation steps for solving an quadratic equation with exponential. A linear function is graphed as a line, has a constant slope, and increases by a constant amount in each time interval. Plot the point that has the given polar coordinates. - Simple and multiple linear regression analysis Therefore, if f (z) is a linear function, then its terms are the directional selection gradients on the discretelongevity scale. A quadratic function is a second-degree polynomial function of the form , where a, b, and c are real numbers and . - Hypothesis tests on proportions Understand Exponential and logarithmic functions, one step at a time. Problem Set: A x-3 (1) For the function f(x)= 4-2x2 evaluate and simplify the following: (i) f(-1) (ii) f(2a-b) (2) The length of a rectangular floor is two metres more than twice its width. To use this website, please enable javascript in your browser. An exponential equation is an equation in which the variable appears in an exponent. You're in the right place! This lesson will discuss each in detail, so it is easy to understand . I start with linear and quadratic functions then extend to exponential and logarithmic functions incorporating asymptotes. Mathematics WEEK TOPICS ASSIGNMENTS OPEN ASSIGNMENTS DUE Week "0.5" 9/7-9/11 * Functions - Linear, Quadratic, Exponential, Logarithmic Functions Problem Set "0.5": Sep. 7 th @ 1:20pm Problem Set " 0.5 ": Sep. 11 th @ 11:59pm Week 1 9/12-9/18 (Session 1) * Sets, Counting Rules, and Summation Notation . - Types of events: elementary, compound, dependent, independent, mutually exclusive, exhaustive, mutually inclusive Designed so you can customize the perfect set for your, This Functions and Graphs Digital Bundle is just what you need to have your students explore the properties, attributes, and key features of the graphs of the following functions: Linear FunctionsQuadratic FunctionsAbsolute Value FunctionsRational FunctionsPolynomial FunctionsLogarithmic FunctionsExponential FunctionsStudents will identify the main properties including intercepts, zeros, asymptotes, standard forms of equations, and more. Just in case you need to have help on division or perhaps graphing, Factoring-polynomials.com is without question the ideal place to head to! 4. Do you see how the exponential function has a backwards "L" shape to it. Exponential Functions . - Zero sum games Solve logarithmic equation; Solve logarithmic equation ie some equations involving logarithms is possible. Test. Various types of equations such as linear, quadratic, trigonometric, exponential equations can be solved using graphical methods. (D)(r,+) Flashcards. 1: Prerequisites Chapter 2: Equations and Inequalities Chapters 3-6: The Algebraic Functions Chapter 3: Functions Chapter 4: Linear Functions Chapter 5: Polynomial and Rational Functions Chapter 6: Exponential and Logarithm Functions Chapters 7-9: Further Study in College Algebra Chapter 7: Systems of Equations and Inequalities Chapter 8: Analytic It is ideally taught after students have learned how to find regressions using a graphing calculator. TI-84 Plus C Silver Edition. Flashcards . 0 Linear or exponential: It costs 40 dollars to join a gym and an additional $10 per month. 6. Then we apply the rules of exponents, along with the one-to-one property, to solve for x: 256 = 4x 5 28 = (22)x 5 Rewrite each side as a power with base 2. The second difference of the y values in the table is the same. Lesson 8.6 - Solving Exponential Equations Using Logs (Examples 5 & 6) - YouTube www.youtube.com. - Methods of fitting trend: free hand, semi-averages, moving averages, least squares methods - Applications of integration to business problems, - Types of sets Linear Programming. Click, Identifying Linear, Exponential, and Quadratic Models, Quadratic and Exponential Equations and Functions, MAT.ALG.908 (Identifying Linear, Exponential, and Quadratic Models - Algebra). Linear Functions . An algebra project with linear, quadratic, and exponential regressions and a quiz. ***NEW***Now includes a reference sheet for students which details the differences between linear, quadratic, and exponential functions. - Interpretation of computer assisted solutions A box of 50 envelopes costs $3.50, and a postage stamp costs$.42. - Value of the game Logarithmic and Exponential Functions - EXERCISE DRAFT. - Activity sequencing and network diagram Worksheets are Comparing linear quadratic and exponential functions, Lesson reteach 11 4 linear quadratic and exponential models, Linearquadraticexponential tables, Comparing linear quadratic and exponential work, Function table linear function l2es1, Classifying tables, Name algebra 1b date linear . Check out this tutorial and learn how to determine is a graph represents a linear, quadratic, or exponential function! Download 8,778. In this activity, students will use a temperature probe to generate a cooling curve and develop an appropriate regression equation to model collected data. A. In functional form, this is written as follows: Multivariable function is that function which involves four or more variables, one dependent variable and three or more independent variables. `exp(x^2-4)=4`, solver shows the calculation steps for solving an quadratic equation with exponential. Students must identify the function name, equation, domain range from a graph. If the price of the consumer product is Sh 40 per Kg, then the total sales revenue, S when Q units of the products are produced and sold is obtained as follows: In this case S is the dependent variable, q the independent variable and 40 is a constant. - Application of mathematical functions in solving business problems, - Types and operations (addition, subtraction, multiplication, transposition and inversion) h+AD)A9IMprppR8%E)rHK9<=}fw;_kDTu)e@ixvgMh)|+#rb Click Create Assignment to assign this modality to your LMS. * I If the data is non-linear, we often consider an exponential or logarithmic model . Linear, Quadratic, and Exponential Functions. - Limitations of game theory, - Basic concepts network, activity, event endstream endobj 91 0 obj <> endobj 92 0 obj <> endobj 93 0 obj <>stream The graph is thus much easier to understand and interpret than a table of values. @momathtchr. Modeling Functions Using Finite Differences. - Forecasting time series value using moving averages, ordinary least squares method and exponential smoothing TI-84 Plus. Use the inverse relationship between exponential functions and logarithms to evaluate expressions and solve . An exponential function is defined as- where a is a positive real number, not equal to 1. A linear function. - Critical path analysis (CPA) endstream endobj startxref Graph Knowledge Linear Quadratic and Exponential from www.harbmath.com. B, F. Advertisement The escape room is perfect for distance learning or digital learning either in small groups, pairs, or individuals. This is an exercise which can be used as a quiz or test or review. `exp(2*x+4)=3`, solver shows details of the calculation of an linear equation with exponential. This function g is called the logarithmic function or most commonly as the natural logarithm. B. Factoring the polynomial, we get: y = ( x + 3) ( x 3) ( x + 2) ( x 2) So the zeroes (that is, the x -intercepts) are at: Particularity: whatever the value of =, an exponential function always passes through the intercept 0,1 . (A)(-r,) Quadratic, Linear, and Exponential Models. - Ordinary derivatives and their applications - Operations of sets: union, intersection, complement and difference Each. In addition to providing the result, the . The variable in the expression of the. 18 = 2x Add 10 to both sides. y = a (7)x 8 = a (7)0 Choose an ordered pair from the table, such as (0, 8). - Assumptions of linear programming Sign up. . Next Lesson. - Advantages and limitations of CPA and PERT, - Components/elements of a queue: arrival rate, service rate, departure, customer behaviour, service discipline, finite and infinite queues, traffic intensity Examples are: This is any quantity whose value remains unchanged in a particular analysis Examples ar. - Application of probability to business problems, - Hypothesis tests on the mean (when population standard deviation is unknown) Played 0 times. Introduction to Functions | Algebra 2, Also included in:Algebra 2 Scavenger Hunt and Activity Bundle, Also included in:Foundations for Functions - Unit 1 Bundle - Texas Algebra 2 Curriculum, Also included in:PreCalculus Unit 1 Functions & Graphs Digital Bundle plus Print, Also included in:Calculus Back to School Review Bundle, Also included in:Functions and Transformations | Digital Interactive Notebook BUNDLE. Base: 5, Answer of exponential: 625, exponent: x. x =. It is easy to see from a graph how as x changes, the value of f(x) is changing. NE.c sQ! Write the function represented by the table. 3. (C)(-r,+3) Get free questions about "Write linear and quadratic functions and exponential functions" to improve your math skills. Time spent on studying in terms of Hours, H. We use the inverse properties to solve both exponential and logarithmic equations: In particular, to solve exponential equations that don't have the same base on both sides of the equal sign, take logs of both sides. (E)(r,+3) Thank you for your interest in this product. Linear, Quadratic & Exponential Functions, Linear, Quadratic and Exponential Functions. 200. . What type of function is: For eg - the exponent of 2 in the number 2 3 is equal to 3. If the base is not base 10, then use. For example, we can only take the logarithm of values greater than 0. hYkOI+1z?;D!^#%~J>,|oWUVJ6QJ5C0=H'C[30H#6!a$ D"OQ@##k` P linear functionsespecially quadratic logarithmic and exponential functionsis from BA MISC at Texas Tech University Algebra and an introduction to functions and their graphs. 100. Solution: Here, the bases are not the same, but we find that we are able to manipulate the right-hand . 1. If you cannot, take the common logarithm of both sides of the equation and then . We can therefore use logarithms to solve exponentials with a missing exponent. C. 2. 2nd Grade Book Summary Worksheet; Art Museum Scavenger Hunt Worksheet; Some filters moved to Formats filters, which is at the top of the page. $$. - Trend projection methods: linear, quadratic and exponential, - Definition of decision variables, objective function and constraints Therefore the inputs of the logarithmic function must be positive. Constant time means that the program will run for the same length of time regardless of the input side. This Functions and Their Graphs Unit Bundle includes guided notes, homework assignments, four quizzes, a study guide and a unit test that cover the following topics: Relations and Functions Implicit vs. Easy to give as a review packet, or separate and turn into stations. - Solving linear programming using graphical method The graphs are purposely tiny so that students are mostly looking for the shape of each. - Comparison and application of forecasts for different techniques It's a simple yet quite practical quiz on one-step equations. `H#4KP. oy 7[Apa%G2j-c!ul1h)Bt";p%Tg4\ck9.4Ev e8:zS6K{4giEV8*|qtZ4Q!%L)Ml)K)O)NH)NLAEQIM1QU*O*NH+NL,NhC"]cdu{s&sf2Q]3mm{@a^e{r=Q8?Ne`CaGW')PuB:Ong:U* O Enter your math expression. When. Which is half its original. - Decision making under risk - expected monetary value, expected opportunity loss, risk using coefficient of variation, expected value of perfect information - Decision making under uncertainty - maximin, maximax, minimax regret, Hurwicz decision rule, Laplace decision rule, - Assumptions of game theory Students will not receive credit for MAT102 if they received credit for a calculus . - Probability trees Functions include linear, quadratic, exponential and logarithmic (with asymptotes). For particular values of x, it is easy to read the values of f(x) and vice versa i.e. Pre-made digital activities. When plotted on an x-y coordinate system, the result is a straight line whose general direction is dependent on the slope, b of the function. gSsSxlf[Nmr0O?HY"_4LC@R++(_b$'*p6,;:&? Recognizing Parent Functions and Function Families Self-Checking Maze! A variable is any quantity that assumes different values in a particular analysis. Section 1-9 : Exponential and Logarithm Equations. - Components of time series (circular, seasonal, cyclical, irregular/ random, trend) linear, quadratic, exponential, logarithmic function graphs, Also included in:PreCalculus Curriculum | All Things Algebra, Also included in:BACK TO SCHOOL | Algebra 1 Curriculum DIGITAL ALL INCLUSIVE Resource Membership, Also included in:FULL UNIT BUNDLE! A printable version is included for your convenience.Your students will analyze and match the graphs of 10 piecewise defined functions. Only $35.99/year. - Regression analysis Solving exponential logarithmic inequalities quadratic linear homework algebra logarithms variables equation exponents tessshebaylo sides. In this activity, students will take a look at 7 different functions and match them to their respective parent function by name: Linear, Absolute Value, Quadratic, Cubic, Reciprocal, Logarithmic, and Exponential. - Hypothesis tests on the difference between means (matched pairs) We give the basic properties and graphs of logarithm functions. - Hypothesis tests on the difference between means (independent samples) - Finite capacity queuing systems (b) Use the graphing utility to graph each model with the original data. - Application of time series x =. Example 1 Solve 7 +15e13z = 10 7 . %%EOF The independent variable is x and the dependent variable is y. a is the constant term or the y intercept. - Crashing of activity/project completion time x2 2x + 1 = 3x 5.
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