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Horizontal Stretches and Compression. Lesson 5.4. Manipulating a Function. Given the function for the Y= screen y1(x) = 0.1(x 3 – 9x 2 ) Use window -10 < x < 10 and -20 < y < 20 Now do the transformation y2(x) = y1(.5x) y3(x) = y1(3x). Set the styles different.

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manipulating a function
Manipulating a Function
  • Given the function for the Y= screeny1(x) = 0.1(x3 – 9x2)
    • Use window -10 < x < 10 and -20 < y < 20
  • Now do the transformation
    • y2(x) = y1(.5x)
    • y3(x) = y1(3x)

Set the styles different

Make predictions for what will happen

manipulating a function3

f(3x)

compressed

f(0.5x)

stretched

Original f(x)

Manipulating a Function
  • For
    • Horizontal stretch
    • Horizontal compression

0 < a < 1

a > 1

changes to a graph
Changes to a Graph
  • Consider once again the effect of modifiers
  • For this lesson we are concentrating on b
  • b => horizontal stretch/compression
    • b > 1 causes compression
    • |b| < 1 causes stretching
changes to a table
Changes to a Table
  • Try these functions
    • y1(x) = 3x2 – 2x
    • y2(x) = y1(0.5 x)
    • y3(x) = y1(2x)
  • Go to tables (Y), then setup, F2
    • Table start = - 4
    • Table increment = 1
changes to a table6

Compressed

Stretched

Changes to a Table
  • Note the results

f(x)

f(0.5x)

f(2x)

changes to a graph7
Changes to a Graph
  • View the different versions of the altered graphs

What has changed?

What remains the same?

changes to a graph8
Changes to a Graph
  • Classify the following properties as changed or not changed when the function f(x) is modified by a coefficient    f(b*x)
functions where formula not known
Functions Where Formula Not Known
  • Given a function defined by a table
    • Fill in all possible blanks
functions where formula not known10
Functions Where Formula Not Known
  • Given f(x) defined by graph below
  • Which is f(2x)? 2*f(x)? f(0.5x)?
assignment
Assignment
  • Lesson 5.4
  • Page 223
  • Exercises 1 – 27 odd