Module 1: Function Transformations

 

Discover
 
Try This 1
  1. On a piece of graph paper, plot the following function. You can use Grid Paper Template, available in the Toolkit, if you like.

     
    This diagram shows a function connecting (–2, 2) to (0, 0) to (2, 2).
  2. Use the original function from question 1 to draw each mapping from the following table. Use a different colour for each mapping or drawing to make your graph(s) easier to read.

    Mapping

    Image Points

    Description of How the Graph Transformed

    Diagram of Transformation

    (x, y) → (3x, y)

     

     

     

    (x, y) → ( x, y)

     

     

     

    (x, y) → (x, 4y)

     

     

     

    (x, y) → (x, y)

     

     

     

    (x, y) → (−2x, y)

     

     

     

    (x, y) → (x, −3y)

     

     

     
  3.  
    1. What effect does multiplying all x-coordinates by a positive constant have on the figure?
    2. What effect does multiplying all y-coordinates by a positive constant have on the figure?
  4. Repeat questions 1 and 2 by using the following function.

     
    This diagram shows a function connecting (–6, 4) to (–4, –4) to (–2, 4).
  5. Revisit question 3. Are your answers still the same?

course folder Save your work in your course folder.

 

Share 1

 

With a partner or group, discuss the following questions based on the information from Try This 1.

  1. How does the graph change when the x-coordinate is multiplied by a value
    1. greater than 1?
    2. between 0 and 1?
    3. that is negative?
  2. How would your answers from question 1 change for a y-coordinate?

course folder If required, save a record of your discussion in your course folder.