## Presentation on theme: "Copyright © 2007 Pearson Education, Inc. Slide 2-1."— Presentation transcript:

Copyright © 2007 Pearson Education, Inc. Slide 2-2 Chapter 2: Analysis of Graphs of Functions 2.1 Graphs of Basic Functions and Relations; Symmetry 2.2 Vertical and Horizontal Shifts of Graphs 2.3 Stretching, Shrinking, and Reflecting Graphs 2.4 Absolute Value Functions: Graphs, Equations, Inequalities, and Applications 2.5 Piecewise-Defined Functions 2.6 Operations and Composition

Copyright © 2007 Pearson Education, Inc. Slide 2-3 2.3 Stretching, Shrinking, and Reflecting Graphs Vertical Stretching of the Graph of a Function If c > 1, the graph of is obtained by vertically stretching the graph of by a factor of c. In general, the larger the value of c, the greater the stretch.

Copyright © 2007 Pearson Education, Inc. Slide 2-4 2.3 Vertical Shrinking Vertical Shrinking of the Graph of a Function If the graph of is obtained by vertically shrinking the graph of by a factor of c. In general, the smaller the value of c, the greater the shrink.

Copyright © 2007 Pearson Education, Inc. Slide 2-5 2.3 Reflecting Across an Axis Reflecting the Graph of a Function Across an Axis For a function (a) the graph of is a reflection of the graph of f across the x-axis. (b) the graph of is a reflection of the graph of f across the y-axis.

Copyright © 2007 Pearson Education, Inc. Slide 2-6 2.3 Example of Reflection Given the graph of sketch the graph of (a) (b) Solution (a) (b)

Copyright © 2007 Pearson Education, Inc. Slide 2-7 2.3 Reflection with the Graphing Calculator

Copyright © 2007 Pearson Education, Inc. Slide 2-8 2.3 Combining Transformations of Graphs Example Describe how the graph of can be obtained by transforming the graph of Sketch its graph. Solution Since the basic graph is the vertex of the parabola is shifted right 4 units. Since the coefficient of is –3, the graph is stretched vertically by a factor of 3 and then reflected across the x- axis. The constant +5 indicates the vertex shifts up 5 units. shift 4 units right shift 5 units up vertical stretch by a factor of 3 reflect across the x-axis