Stretching%20and%20Shrinking%20Graphs

1
Lesson 8.4

• Stretching and Shrinking Graphs
• To discover how to change the shape of polygons
  and functions
• To explore vertical stretches and shrinks of
  polygons and graphs of equations
• To write equations for graphs resulting from
  stretches and shrinks

2

• Imagine what happens to a picture on a rubber
  sheet as you stretch it vertically

3

• Imagine what happens to a picture if the width
  stays the same and we shrink the picture
  vertically.

You already know how to translate and reflect
graphs on the coordinate plane. Lets see how to
change their shape.
4
Changing the Shape of a Graph

• Name the coordinates of the vertices of this
  quadrilateral.
• Graph the quadrilateral on your calculator. Use
  L1 for the x-coordinates of the vertices and L2
  for the y-coordinates of the vertices.
• Each member of your groups should choose one
  value of a 2, 3, 0.5, or -2. Use your value of
  a to define two new lists
• L3 L1
• L4 aL2

5

• Graph the second quadrilateral using L3 and L4.
• Share your results from the last step. For each
  value of a, describe the transformation of the
  parent quadrilateral. What was the result for
  each vertex?
• Predict the location of each vertex if the value
  of a is 1.5. Describe how you think the overall
  appearance of the quadrilateral will change.
• Make a conjecture about how a graph will be
  affected when its y-values are multiplied by
  values greater than 1, between 0 and 1, and less
  then 0.

6

• Graph this triangle on your calculator. Use L1
  for the x-coordinates of the vertices and L2 for
  the y-coordinates of the vertices.
• Describe how these transformations will transform
  the triangle.
• Transformation 1
• L3L1
• L4-0.5L2
• Transformation 2
• L3L1
• L42L2 - 2

7

• Write definitions for L3 and L4 in terms of L1
  and L2 to create each image.

8

• Next, see how you can stretch and shrink the
  graph of a function.
• Each member of your group should choose an
  equation from the list below. Enter the equation
  in your y1 and graph it.
• Y1-10.5x
• Y1-x2 1
• Y1x
• Y11.4x
• Enter y22Y1(x) and graph it.
• Look at a table and compare the values of y1 and
  y2.

9

• Repeat the last steps for
• Y20.5y1(x)
• Y23y1(x)
• Y2-2y1(x)
• Write an equation for R(x) in terms of B(x).
  Then write an equation for B(x) in terms of R(x)