Download MATH 1101 Test #3 Review Sheet: Functions, Slope, and Linear Equations and more Exams Mathematics in PDF only on Docsity! MATH 1101 Test #3 Review Sheet You should know definitions of the following: Function, domain, codomain, range Slope You should be able to use function notation Given that f is a function of x, you should be able to interpret/define expressions such as What is f(3)? What is the value of the function f at the input 3? Find all x satisfying f(x) = 8; For what input(s), if any, does the function f have a value of 8? 3.1: S-1, S-3, S-5, S-7, S-9; 1, 3, 5, 9, 11, 13 Definition of Slope: The slope (of a function) is the signed vertical change (of the function) corresponding to a one unit increase in the horizontal coordinate Characterization of lines Slope is rise/run ; Slope is (signed vertical change)/(signed horizontal change) Using these relationships to answer questions about lines or contexts that are “linear” 3.2: S-1, S-3, S-5, S-7, S-9; 1, 3, 9, 11, 19 Equation of a line Point-slope form (y-y1) = m (x-x1) where m is the slope and (x1, y1) is a point on the line Slope-intercept form y = mx + b where m is the slope and (0,b) is the vertical intercept Linear Function: L(x) = mx + b where m is the slope and (0,b) is the vertical intercept of the line Given a point and the slope, finding an equation of the line or linear function Given more than one point, finding an equation of the line or linear function In short, seeing the connection between the context and the linear function modeling the context Interpreting the slope in the context of a given problem that is “linear” Interpreting a point on the line in the context of a given problem that is “linear” Expressing statements in context in terms of the linear function using function notation 3.3: S-1, S-3; 1, 3, 7, 11, 13 Be able to tell whether or not there exists a line that passes through three or more given points Given a table of three or more points for which there exists a line that passes through all of them, finding the slope of the corresponding line or linear function finding equations of the corresponding linear function finding the second coordinate of a point on the line given its first coordinate finding the first coordinate of a point on the line given its second coordinate In short, seeing the connection between the context and the linear function modeling the context Interpreting the slope in the context of a given problem that has a linear model Interpreting a point on the linear model in the context of a given problem Expressing statements in context in terms of the linear function using function notation Finding the unknown coordinate of a point on a linear model given one of its coordinates typically the coordinates will be given in terms of the context Being able to translate information in the context to the linear function and vice versa 3.4: S-1, S-11; 1, 3, 5, 7, 9, 13 You should be able to describe the intuitive idea behind the linear regression What is the “penalty” function that we minimize? Illustrate with a schematic Be able to use the calculator to construct the linear regression model Be able to draw a graph with the data [points] and the regression model Be able to use the regression model to approximate values not in the table
