Functions+and+their+graphs

Created and Designed by Mr. Bartok and Ms. Leshay Name:bolin wang Date:11/3/2011 1. Create the necessary functions to graph a Winchendon “W” (as close to the picture below as you can get). y=|x| y2=2x+3

2. Label each function using function notation. [f(x)=?, g(x)=?, h(x)=?, etc. ] f(x)=|x| g(x)=2x+3

3. Identify the parent functions used. I used the abs function, made x just postive, the graph will be V. The one line across the V, it is y=kx+b.

4. Explain the transformations made for each. The W can be two parts, two V. So it is y=|x| and y=|x-5|, don't care about the across point, it is a W. For the line cross the W, it is y2=2x+3.

5. Label the domain and range of each function, notice the picture only uses parts of lines. y=|x| x=R y=2x+3 x≠0

6. Finally classify each function as continuous, discontinuous, or discrete over your specified domains. If we just cut a part of the graph, the W should be inside of the graph. The point (2,2), we just leave the part under this point, and cut the part on the top of this point. It will be a W.

7. Include the resulting graph of your functions in your solutions with each of them clearly labeled. The y=|x|, and y2=|x-5|, it is parallel, and we cut the top part, whinch is on the point(2,2), it is also the crose of the two graph. Then we can see a W. If we want have a beautiful W. we can just leave the part of under(-2.2) and (7,2).

REMEMBER: Use the proper format for typing your creative assessment (problem statement, methods, solution, generalizations, self-assessment). HINT: For generalizations look for patterns in transformations and try to create rule(s) for the function’s behavior.