1 / 14

Chapter 3: Transformations of Graphs and Data

Chapter 3: Transformations of Graphs and Data. Lesson 5: The Graph Scale-Change Theorem Mrs. Parziale. Vocabulary:. Vertical stretch : A scale change that makes the original graph taller or shorter Horizontal stretch : a scale change that makes the original graph wider or skinnier.

ciqala
Download Presentation

Chapter 3: Transformations of Graphs and Data

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 3: Transformations of Graphs and Data Lesson 5: The Graph Scale-Change Theorem Mrs. Parziale

  2. Vocabulary: • Vertical stretch:A scale change that makes the original graph taller or shorter • Horizontal stretch:a scale change that makes the original graph wider or skinnier. • Scale change:a stretch or shrink applied to the graph vertically or horizontally • Vertical scale change: The value that changes the vertical values of the graph. • Horizontal scale change:The value that changes the horizontal values of the graph. • Size change:When the same vertical and horizontal scale change occurs.

  3. Example 1: Consider the graph of (a) Complete the table and graph on the grid:

  4. (b) Replace (y) with . 1. Solve the new equation for y and graph it on the same grid at right. 2. What happens to the y-coordinates? 3. This is called a vertical stretch of magnitude 3 . 4. Under what scale change is the new figure a vertical scale change of the original?

  5. (c) Replace (x) with . 1. Solve the new equation for y and graph it. 2. What happens to the x-coordinates? • This is called a horizontal stretch of magnitude 2 . • Under what scale change is the new figure a horizontal scale change of the original?

  6. (d) Let . Find an equation for g(x), the image of f(x) under What is happening to each part of the graph?

  7. How is the x changed? • Change: horizontal stretch two times wider. • How is the y changed? • Change: vertical stretch three times the original.

  8. Graph Scale-Change Theorem In a relation described by a sentence in (x) and (y), the following two processes yield the same graph: (1) replace (x) by and (y) by in the sentence (2) apply the scale change __________________ to the graph of the original relation. Note: If a = b, then you have performed a __________ size change If a = negative, the graph has been reflected (flipped) over the y-axis If b = negative, the graph has been reflected over the x-axis

  9. So, What’s the Equation? (d) Find an equation for g(x), the image of f(x) under

  10. Example 2: • Consider . Find an equation for the function under • Describe what happens to all of the x values: • Describe what happens to all of the y values:

  11. Find the equation for the transformed image by • Replace (x) with ______________ • Replace (y) with ______________ • Now make the new equation (remember to simplify to y= form):

  12. Graph It!

  13. Closure - Example 3: The graph to the right is y = f(x). Draw . • What should happen to all of the x values? • What should happen to all of the y values?

More Related