1. AIM: WHAT IS A PIECEWISE DEFINED FUNCTION? HW P. 25 #37, 39, 95, 97, P. 39#43, 48 1 EX) Sketch the Piecewise-Defined Function BY HAND x2x+3y 12(1)+35 02(0)+32 2(-1)+31 For each function, start at the domain and work your way up/down Note: f(x) is not connected at x = 1 x-x+4y 1-1+33 2-2+32 3-3+31 A Piecewise-Defined Function is: A function defined in pieces for certain x-values

2. AIM: WHAT IS A PIECEWISE DEFINED FUNCTION? HW P. 25 #37, 39, 95, 97, P. 39#43, 48 2 EX) Evaluate the piecewise-defined function at x = -1 and x = 0 Graph the piecewise function on the calculator: Divide out the domain; the domain acts as a Boolean – as long as it is true the value is 1, and when it is false the value is 0. Therefore, where the calculator tries to graph the function beyond the domain, it attempts to graph the function by 0, which is undefined.

3. AIM: WHAT IS A PIECEWISE DEFINED FUNCTION? HW P. 25 #37, 39, 95, 97, P. 39#43, 48 3 EX) Sketch the Piecewise-Defined Function

4. AIM: WHAT IS A PIECEWISE DEFINED FUNCTION? HW P. 25 #37, 39, 95, 97, P. 39#43, 48 4 a) Write the function below as a Piecewise-Defined Function b) Sketch the graph by hand c) Find the area of the region bounded by the function and the line y = 5

5. AIM: WHAT IS A PIECEWISE DEFINED FUNCTION? HW P. 25 #37, 39, 95, 97, P. 39#43, 48 5 b) Sketch the graph by hand c) Find the area of the region bounded by the function and the line y = 5 Split up the region into right triangles and determine the lengths of the legs. 3 33 4-2 For this particular example, it was not important to perform the step above, however there will be examples in which the lengths of the legs are not as evident. The above process would then be necessary to correctly determine the lengths of the legs or the distance between 2 points. A1A2

6. AIM: WHAT IS A PIECEWISE DEFINED FUNCTION? HW P. 25 #37, 39, 95, 97, P. 39#43, 48 6 a) Write the function below as a Piecewise-Defined Function b) Sketch the graph by hand c) Find the area of the region bounded by the function and the line y = 6.8

7. AIM: WHAT IS A PIECEWISE DEFINED FUNCTION? HW P. 25 #37, 39, 95, 97, P. 39#43, 48 7 6.8 13.6 4.8 -8.8

8. AIM: WHAT IS A PIECEWISE DEFINED FUNCTION? HW P. 25 #37, 39, 95, 97, P. 39#43, 48 8 a) Write the function below as a Piecewise-Defined Function b) Sketch the graph by hand c) Find the area of the region bounded by the function and the x-axis from x=-4 to x=0 A1A2

9. AIM: WHAT IS A PIECEWISE DEFINED FUNCTION? HW P. 25 #37, 39, 95, 97, P. 39#43, 48 9 a) Write the function below as a Piecewise-Defined Function b) Sketch the graph by hand c) Find the area of the region bounded by the function and the x-axis from x = -3 to x = 5.

10. AIM: WHAT IS A PIECEWISE DEFINED FUNCTION? HW P. 25 #37, 39, 95, 97, P. 39#43, 48 10 Review for next test. Know how to: Graph piecewise functions by hand Graph piecewise functions on calc Re-write an absolute value equation as a piecewise function Find the area under a specified region on the x and y axes Write a function in terms of a specified variable (see function apps sheet) Re-write as a piecewise function: Graph by hand and on calc: Find area between function and x-axis, from x = -5 to x = 5:

11. AIM: WHAT IS A PIECEWISE DEFINED FUNCTION? HW P. 25 #37, 39, 95, 97, P. 39#43, 48 11 #39: Evaluate f(-2), f(1), and f(2) and graph

12. AIM: WHAT IS A PIECEWISE DEFINED FUNCTION? HW P. 25 #37, 39, 95, 97, P. 39#43, 48 12 #95, 97: Write a piecewise-defined functions for each of the graphs: #43: Sketch the graph of the piecewise-defined functions: #48: Sketch the graph of the piecewise-defined functions: