Presentation on theme: "Chapter 3: Transformations of Graphs and Data"— Presentation transcript:
1Chapter 3: Transformations of Graphs and Data Lesson 5: The Graph Scale-Change TheoremMrs. Parziale
2Vocabulary:Vertical stretch: A scale change that makes the original graph taller or shorterHorizontal stretch: a scale change that makes the original graph wider or skinnier.Scale change: a stretch or shrink applied to the graph vertically or horizontallyVertical 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.
3Example 1:Consider the graph of (a) Complete the table and graph on the grid:xy-2-112
4(b) Replace (y) with1. 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?
7How is the x changed?Change: horizontal stretch two times wider.How is the y changed?Change: vertical stretch three times the original.
8Graph 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 changeIf a = negative, the graph has been reflected (flipped) over the y-axisIf b = negative, the graph has been reflected over the x-axis
9So, What’s the Equation?(d) Find an equation for g(x), the image of f(x) underxy-2-131-32xy