3.6 Combination of Transformations Notes_Alg1

3.6 Combination of Transformations Notes_Alg1

Combining Transformations

The functions we typically work with involve multiple transformations from its parent function. Use the transformation rules we have talked about previously to describe all the transformations.

Graph f(x) = x and g(x) = -2x + 3. Describe the transformations from f(x) to g(x).

• Since f(x) = x we can rewrite g(x) as g(x) = -2f(x) + 3

• Look for the transformations that occurred.

• f(x) was multiplied by a -2 which represents two transformations...

• vertical stretch by a factor of 2 and a

• reflection over the x-axis

• 3 was also added to f(x) which is a....

• vertical translation up 3 units

Multiple Choice

f(x) = x

g(x) = 4x - 5

Describe the transformations from f(x) to g(x).

• vertical shrink by a factor of 4

  vertical translation up 5 units

• vertical shrink by a factor of 4

  horizontal translation right 5 units

• vertical stretch by a factor of 4

  vertical translation down 5 units

• vertical stretch by a factor of 4

  horizontal translation left 5 units

Multiple Choice

f(x) = x
g(x) =  $-\frac{1}{4}x+2$  
Describe the transformations from f(x) to g(x).

• Vertical shrink by a factor of - 1/4

  
  
  

  Vertical translation up 2 units

• Vertical shrink by a factor of 1/4
  
  Reflection over the x-axis

  
  

  Vertical translation up 2 units

• Vertical stretch by a factor of 1/4

  
  

  Reflection over the x-axis

  
  

  vertical translation up 2 units

• Vertical stretch by a factor of -1/4

  
  

  horizontal translation left 2 units