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Alg 2 BC – U2 Day 3 – Piecewise Functions Remember: A piecewise function is composed of pieces of other functions. x 5, For example: f ( x) 2 x 1, 2 x 9, x 2 2 x 2 x2 Graph it below and find f(-10), f(0) and f(10). Sometimes, piecewise functions are continuous like above, where all of the pieces are connected. Sometimes a piecewise function consists of pieces that are not connected. 3, For example: f ( x) x 1, 4 x, x0 0 x2 x2 Graph it below and find f(0) and f(2). Try to write a piecewise function for the graph below! A special type of piecewise function is the Greatest Integer Function. It is denoted as f(x) = x . To see what this graph looks like, graph: y = int(x) Can you tell, by looking at the graph, what x does? Using the TABLE function: Choose 2nd TBL SET: Experiment to see if you can determine what each of the following mean: (To see the table, you need to choose TABLE after doing TBL SET.) TblStart Tbl Indpndt: AUTO ASK Depend: AUTO ASK-+ Now use the TABLE function to fill in the chart below for f(x) = x X 0 0.1 0.2 0.5 0.9 0.999 1 Y We can graph any greatest integer function by simply making a table of values. We could also use transformations, but we’ll get to that in a few days. Example: y x 2 y 3 x Extra info: Graphing a Piecewise Function on the Calculator: x 5, For f ( x) 2 x 1, 2 x 9, x 2 2 x 2, x2 y1 ( x 5) / ( x 2) the notation would be y 2 (2 x 1) / ( 2 x and x 2) . y3 (2 x 9) / ( x 2) The greater than and less than symbols can be found under the TEST menu (2nd MATH). 3, Try: f ( x) x 1, 4 x, x0 0 x2 x2 Homework Worksheet: Graph each piecewise function by hand: 2 x 3, x 1 1. f ( x) 1, 2 x 1 x 1, x 2 3x 4, x 2 2. f ( x) 1 x 3, x 2 2 Graph each function by hand by making a table of values: 3. f ( x) x 2 5. Write a piecewise function for this graph: 4. f ( x) 2 x 1