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1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-1 Graphs and Functions Chapter 3

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2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-2 3.1 – Graphs 3.2 – Functions 3.3 – Linear Functions: Graphs and Applications 3.4 – The Slope-Intercept Form of a Linear Equation 3.5 – The Point-Slope Form of a Linear Equation 3.6 – The Algebra of Functions 3.7 – Graphing Linear Inequalities Chapter Sections

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3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-3 § 3.3 Linear Functions: Graphs and Applications

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4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-4 Graph Linear Functions Linear Function A linear function is a function of the form f(x) = ax + b The graph of any linear equation is a straight line. The domain of any linear function is all real numbers. If a ≠ 0, then the range of any linear function is all real numbers.

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5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-5 Graph Linear Functions Using Intercepts Standard Form of Linear Equation The standard form of a linear equation is ax + by = c where a, b, and c are real numbers, and a and b are not both 0.

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6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-6 Graph Linear Functions Using Intercepts x- and y-intercepts The x-intercept is the point at which a graph crosses the x-axis. The x- intercept will always be of the form (x, 0). The y-intercept is the point at which a graph crosses the y-axis. The y-intercept will always be of the form (0, y).

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7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-7 Graph Linear Functions Using Intercepts To Graph Linear Equations Using the x- and y- intercepts 1.Find the y-intercept. Set x equal to 0 and find the corresponding value for y. 2.Find the x-intercept. Set y equal to 0 and find the corresponding value for x. 3.Plot the intercepts. 4.Draw the line. Using a straightedge, draw a line through the points. Draw an arrowhead at both ends of the line.

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8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-8 Graph Using Intercepts This gives us the y-intercept (0, 2). Example: Graph 5x = 10y – 20 using the x- and y- intercepts. Solution To find the y-intercept, set x = 0 and solve for y.

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9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-9 Graph Using Intercepts This gives us the x-intercept (-4, 0). Use the intercepts (0, 2) and (-4, 0) to graph the linear function. To find the x-intercept, set y = 0 and solve for x.

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10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-10 Graph Using Intercepts Plot the points and draw the line.

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11 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-11 Graph Equations of the Form x = a and y = b Equations of a Horizontal Line The graph of any equation of the form y = b will always be a horizontal line for any real number b. Equations of a Vertical Line The graph of any equation of the form x = a will always be a vertical line for any real number a.

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