1. Everyone needs a small white board, marker, and eraser rag 1

2. Graphing Piecewise Functions

3. 3 Objectives I can evaluate piece-wise functions I can graph piece-wise functions

4. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 4 WISE FUNCTIONS These are functions that are defined differently on different parts of the domain.

5. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 5 An important type of function is called a "piecewise" function, so called because, well, it's in pieces: Piecewise functions {  --Piece 1  --Piece 2 As you can see, this function is split into two halves: the half that comes before x = 1, and the half that goes from x = 1 to infinity Which half of the function you use depends on what x is

6. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 6 { Suppose we want to find f(3) which half would we use? Suppose we want to find f(0) which half would we use?

7. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 7 Now You Try: Practice Problem { Given: 7 9

8. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 8 x y 4 -4 A piecewise-defined function is composed of two or more functions. Piecewise-Defined Functions f(x) = 3 + x, x < 0 x 2 + 1, x 0 Use when the value of x is less than 0. Use when the value of x is greater or equal to 0. (0 is not included.) open circle (0 is included.) closed circle

9. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 9 Graphing Piecewise functions Domain of the blue Expression. Domain of the red Expression. {

10. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 10 This means for x’s less than 0, put them in f(x) = -x but for x’s greater than or equal to 0, put them in f(x) = x 2 What does the graph of f(x) = -x look like? Remember y = f(x) so let’s graph y = - x which is a line of slope –1 and y-intercept 0. Since we are only supposed to graph this for x< 0, we’ll stop the graph at x = 0. What does the graph of f(x) = x 2 look like? Since we are only supposed to graph this for x  0, we’ll only keep the right half of the graph. Remember y = f(x) so lets graph y = x 2 which is a square function (parabola) This then is the graph for the piecewise function given above.

11. Practice Graph the following piece-wise functions on the grid side of your white boards 11

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16. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 16 Homework WS 1-8