 # Copyright © 2011 Pearson Education, Inc. Slide 2.3-1 2.3 Vertical Stretching Vertical Stretching of the Graph of a Function If a point lies on the graph.

## Presentation on theme: "Copyright © 2011 Pearson Education, Inc. Slide 2.3-1 2.3 Vertical Stretching Vertical Stretching of the Graph of a Function If a point lies on the graph."— Presentation transcript:

Copyright © 2011 Pearson Education, Inc. Slide 2.3-1 2.3 Vertical Stretching Vertical Stretching of the Graph of a Function If a point lies on the graph of then the point lies on the graph of If then the graph of is a vertical stretching of the graph of by applying a factor of c.

Copyright © 2011 Pearson Education, Inc. Slide 2.3-2 2.3 Vertical Shrinking Vertical Shrinking of the Graph of a Function If a point lies on the graph of then the point lies on the graph of If then the graph of is a vertical shrinking of the graph of by applying a factor of c.

Copyright © 2011 Pearson Education, Inc. Slide 2.3-3 2.3 Horizontal Stretching and Shrinking Horizontal Stretching and Shrinking of the Graph of a Function If a point lies on the graph of then the point lies on the graph of (a)If then the graph of is a horizontal stretching of the graph of (b) If then the graph of is a horizontal shrinking of the graph of

Copyright © 2011 Pearson Education, Inc. Slide 2.3-4 2.3 Reflecting Across an Axis Reflecting the Graph of a Function Across an Axis For a function defined by the following are true. (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 © 2011 Pearson Education, Inc. Slide 2.3-5 2.3 Example of Reflection Given the graph of sketch the graph of (a) (b) Solution (a) (b)

Copyright © 2011 Pearson Education, Inc. Slide 2.3-6 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