Horizontal Stretches and Compression Lesson 5 4 Manipulating

Horizontal Stretches and Compression Lesson 5. 4

Manipulating a Function • Given the function for the Y= screen y 1(x) = 0. 1(x 3 – 9 x 2) § Use window -10 < x < 10 and -20 < y < 20 • Now do the transformation § y 2(x) = y 1(. 5 x) § y 3(x) = y 1(3 x) Set the styles different Make predictions for what will happen

Manipulating a Function f(3 x) compressed f(0. 5 x) stretched Original f(x) • 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 Note Science Illustration on the Web § b > 1 causes compression § |b| < 1 causes stretching

Changes to a Table • Try these functions § y 1(x) = 3 x 2 – 2 x § y 2(x) = y 1(0. 5 x) § y 3(x) = y 1(2 x) • Go to tables ( Y), then setup, F 2 § Table start = - 4 § Table increment = 1

Changes to a Table • Note the results f(x) f(0. 5 x) f(2 x) Compressed Stretched

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) Property Zeros of the function Intervals where the function increases or decreases X locations of the max and min Changed Not Changed Y-locations of the max and min Steepness of curves where function is increasing/decreasing

Functions Where Formula Not Known • Given a function defined by a table § Fill in all possible blanks x -3 -2 -1 0 1 2 3 f(x) -4 -1 2 3 0 -3 -6 f(. 5 x) f(2 x)

Functions Where Formula Not Known • Given f(x) defined by graph below • Which is f(2 x)? 2*f(x)? f(0. 5 x)?

Assignment • Lesson 5. 4 • Page 223 • Exercises 1 – 27 odd