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Lesson 8.4

Explore vertical stretches and shrinks of polygons and graphs of equations, learn to write equations for resulting graphs, and discover how shape changes with different transformations.

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Lesson 8.4

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  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. Let’s 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 = a•L2

  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 • L3=L1 • L4=-0.5•L2 • Transformation 2 • L3=L1 • L4=2•L2 - 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=-1+0.5x • Y1=-x2 +1 • Y1=|x| • Y1=1.4x • Enter y2=2•Y1(x) and graph it. • Look at a table and compare the values of y1 and y2.

  9. Repeat the last steps for • Y2=0.5•y1(x) • Y2=3•y1(x) • Y2=-2•y1(x) • Write an equation for R(x) in terms of B(x). Then write an equation for B(x) in terms of R(x)

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