Transformation of a Piecewise Function 1.1 2003/07/09 17:09:42 GMT-5 2003/07/19 19:17:37 GMT-5 Debbie Trahan debtrahan@aol.com Debbie Trahan debtrahan@aol.com Kyle Clarkson kclarks@rice.edu piecewise function Transformations In this module students will investigate transformations on a piecewise function.

In this module, you will investigate the transformations on a piecewise function.

The graph of the function f shown in figure 1 consists of two line segments.

Use function f shown in figure 1 to answer the questions in this lesson.

Find f -1 . Read the point from the graph. f -1 0 Estimate f 1.25 from the graph then find the exact answer algebraically. Estimated answer will vary. Write an equation for f when 0 x 2 y -3 x 3 Substitute 1.25 in place of x and solve for y . y -3 1.25 3 f 1.25 -0.75 Write a piecewise function for f . f x 3 x 3 -2 x 0 -3 x 3 0 x 2 Find the value of x when f x -2 . x -5 3 or x 5 3 For what values of x is f increasing? -2 0 Find the domain of f . -2 2 Find the minimum value of f . -3 Find the maximum value of f . 3 Find the area of the region beneath f in the first quadrant. 1.5 square units Find the area of the region bounded by f , x 0 , x 1 2 , and y 0 . 1.125 square units Part a: Graph f x 1 then find the maximum and the minimum value of f x 1 . Part b: Find the area of the region beneath f x 1 in the first quadrant. Part a:

The maximum value is 3 . The miminimum value is -3 . Part b: 3 square units . Part a: Graph f x 2 then find the x - intercepts of the graph and the maximum and the minimum value of f x 2 . Part b: Find the area of the region beneath f x 2 in the first quadrant. Part a:

The x - intercepts of the graph are -5 3 and 5 3 . The maximum value is 5 The minimum value is -1 Part b: 25 6 square units . Graph f x .

Graph 1 3 f x .

Graph f 2 x .

Graph f 2 x 2 .

Graph f x 1 .