Horizontal Stretches and Compression

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# Horizontal Stretches and Compression - PowerPoint PPT Presentation

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 &lt; x &lt; 10 and -20 &lt; y &lt; 20 Now do the transformation y2(x) = y1(.5x) y3(x) = y1(3x). Set the styles different.

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## PowerPoint Slideshow about 'Horizontal Stretches and Compression' - kimball

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### Horizontal Stretches and Compression

Lesson 5.4

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

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
• 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
• 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

Compressed

Stretched

Changes to a Table
• Note the results

f(x)

f(0.5x)

f(2x)

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

What has changed?

What remains the same?

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
• Given a function defined by a table
• Fill in all possible blanks
Functions Where Formula Not Known
• Given f(x) defined by graph below
• Which is f(2x)? 2*f(x)? f(0.5x)?
Assignment
• Lesson 5.4
• Page 223
• Exercises 1 – 27 odd