Transformations of Functions (Chapter 2.3-page 97)

Learning Goals: Determine, through investigation using technology, the roles of the parameters a, k, d, and c in functions of the form y = af(k(x – d )) + c, and describe these roles in terms of transformations on the graphs of f(x) = x,,, and and state the domain and range of the transformed functions

Review: Horizontal and Vertical Translations

Graph the following set of functions,, on the same set of axes. Compare the equations/graphs of g(x ) and h(x ) to the equation of f(x ). Describe any similarities and differences Share with a partner

Describe how the value of d in changes the graph of f (x ).

Try these graphs: Compare the equations/graphs of g(x ) and h(x ) to the equation of f(x ). Describe any similarities and differences Share with a partner

What about these graphs: Compare the equations/graphs of g(x ) and h(x ) to the equation of f(x ). Describe any similarities and differences Share with a partner

Given sketch the graph of by determining image points for any original key points.

Write as f(x) : ( x, y)g(x) : ( x + 3, y) ( 0, 0 )( 0 – 3, 0 ) = ( -3, 0 ) ( 1, 1 )( 1 - 3, 1 ) = ( -2, 0 ) ( 4, 2 )( 4 – 3, 2 ) = ( 1, 2 ) ( 9, 3 )( 9 – 3, 3 ) = ( 6, 3 )

Graph by using image points: Compare the equations/graphs of g(x ) and h(x ) to the equation of f(x ). Describe any similarities and differences Share with a partner

Write f(x) : ( x, y)g(x) : ( x, y + 3) ( 0, 0 )( 0, ) = ( 0, 3 ) ( 1, 1 )( 1, ) = ( 1, 4 ) ( 4, 2 )( 4, ) = ( 4, 5 ) ( 9, 3 )( 9, ) = ( 9, 6 )

Describe the transformation from the base function f(x) to sketch the graph of g(x) and then state the domain and range of each function.

This is a horizontal translation of 2 units to the left ( ) and a vertical translation of 3 units up ( ). f(x) : ( x, y)g(x) : ( x - 2, y + 3) ( 0, 0 )( 0 - 2, ) =( - 2, 3 ) ( 1, 1 )( 1 - 2, ) = ( - 1, 4 ) ( 2, 4 )( 4 - 2, ) = ( 2, 5 ) ( 3, 9 )( 9 - 2, ) = ( 7, 6 )

More Practice/ Homework: Read Examples on pages Read Key concepts on page 101 Page 102: # 1, 2, 4, 3 – 6 (a,d), 8 Work with a partner Then share with the class