1. World 2-3 Transformations of a Function

2. Recall that in the past you have encountered functions of degrees 0 and 1. DegreeFunction Type 0 f(x) = bConstant 1 f(x) = x Linear 2 f(x) = x 2 Quadratic 3 f(x) = x 3 Cubic 0.5 Squareroot All of these functions can be modified by translating, rotating, stretching, compressing or flipping/mirroring. The general form of these modifications is f(x)=a(x-h) n + k 0o0o 1o1o 2o2o 3o3o 0.5 o

3. Eg 1. Changing k: Vertical Shift  or  f(x)=a(x-h) n + k f(x) = x f(x) = x + 5 f(x) = x - 4 Changing k causes a vertical shift up or down. f(x) = x 2 f(x) = x 2 + 4 f(x) = x 2 - 7

4. Changing a causes the graph to stretch or compress vertically. Eg 2. Changing a: Vertical Stretch or Compression f(x)=a(x-h) n + k y =x 2 y = 2x 2 y = 1/4x 2

5. Eg. 3. Changing h: Horizontal Shift f(x)=a(x-h) n + k y =x 2 y =(x+4) 2 y = (x-5) 2 If h > 0: shift left h unitsIf h < 0: shift right h units

6. Eg 4. Sign of a: Vertical Flip or Mirror through the x axis f(x)=a(x-h) n + k y =x 2 y = -x 2 y =x y =-x If a > 0: function goes up If a < 0: function goes down 

7. Vertical Shift Horizontal Shift Vertical Stretch Vertical Flip Ex. 5 Determine the transformations Vertical stretch, factor 2 Horizontal shift, right 3 V stretch, factor 3 V shift up 10 units Vertical Flip Vertical Stretch, factor 2 Vertical Shift, down 4 Horizontal shift, 3 right

8. Homework Complete Handout