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Algebra II
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Algebra II

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  1. Algebra II Chapter 2 Linear Equations and Functions

  2. Section 2.1 Functions and their Graphs • Definitions • Relation • Function • Domain • Range • Representing Relations and Functions • Mapping diagram • Ordered Pairs • Points on the coordinate plane • Equations • Graphing equations – table of values, other methods • Solutions, Independent and Dependent variables • Vertical Line Test • Functional Notation • Examples/Problems

  3. Sec 2.2 Slope and Rate of ChangeSec 2.3 Quick Graphs of Linear Equations • Slope • How do you measure it? • What do you need to calculate it? • Slopes of horizontal and vertical lines • Slopes of parallel and perpendicular lines • Slope and ‘Rate of Change’ • Graphs of Linear Equations • How to recognize an equation as linear • Terminology • Forms of lines • Graphing lines • Slope intercept form • Standard form • Point-slope form • Table of values • Converting forms

  4. Activity 2.3: Using TechnologyGraphing Lines on the TI-83+/84 • Activity is on Pg 90 • We’ll graph linear equations on the graphing calculator • Steps • Clear all plots • Solve for y • Set your viewing window • Graph

  5. Section 2.4 Writing Equations of Lines • Given the following information • Slope and y-intercept; or • Slope and a point; or • Two points on the line • We’ll write equations in the following forms • Slope-intercept • Point-slope • Standard • And we’ll be able to convert from one form to another • We’ll also review ‘direct variation’ y=kx • Constant of variation • How to recognize if a set of points show constant variation

  6. Sec 2.5 Correlation and Best Fitting Lines • Activity 2.5 Developing Concepts • Fitting a line to a set of data pg. 99 • Correlation between variables • Relationship between variables • Positive, negative and no correlation • Linear and non-linear correlation • Graphical display of correlated data • Scatterplots • Fitting a line to data • Draw scatterplot • Fit line to data • Choose 2 points on the fitted line • Find equation of line given these 2 points • Using your fitted line to make estimates • Interpolation vs extrapolation

  7. Section 2.6 Linear Inequalities in Two Variables • What is a linear inequality in 2 variables • How do you graph it? • Boundary line • Shade a half-plane • Graph a linear inequality in 1 variable • What does the shaded region represent? • Examples and word problems

  8. Section 2.6 Linear Inequalities in 2 Variables • Linear inequality in one variable • Graph solution set • Linear Equation in two variables • How to recognize a linear equation • Graphing a linear equation • The graph as a solution set • Linear Inequality in two variables • How to recognize a linear inequality • Graphing a linear inequality • Graph the boundary of the inequality • Shade one of the half-planes • The solution set • Skills • How to graph an inequality • Given a graph provide the inequality • Vocabulary • Word Problems

  9. Section 2.7 Piecewise Functions • Until now, representing functions as a single equation • Recognizing a piecewise function from a graph • Writing a piecewise function • Recognizing domain and range • Recognizing a piecewise function in algebraic notation • Graphing a piecewise function • Recognizing domain and range • Evaluating a piecewise function • Using piecewise functions in word problems

  10. Section 2.8: Absolute Value Functions • The shape of absolute functions • The general form of an absolute value function • vertex (x, h) • Sign of a • Value of a • Graphing an absolute value function • Writing the absolute value function given the graph