This is day two of partner presentations on the transformation of a given function from its parent function. The first day was given to students to prepare their presentations, so the second day is to allow all groups of students to present if possible. Each set of partners takes about five minutes to present. This is the first presentation of the year, so I do not set a certain time limit on the presentation. I expect the students to cover the details stated in the Rubric for the Parent Transformation Presentation and I intend for each presentation to take about five minutes.
The goal of the presentations is for students to become familiar with the graphing vocabulary and to apply it to given functions. It reduces the fear of testing and allows students to explore in a more relaxed environment. As well as for students to see the common transformations made within function families. Students being able to see how equations are connected to shifting right, left, up, down will help students be more successful when we study each individual function more in depth later in the year. I did not give students functions that were horizontally stretched or shrunk, or reflected across the y-axis. I will present these transformations when we study each individual function later in the year.
This is a sample of one of the Parent Function Transformation Presentations. The students have been given the function y=2^x - 6. The two students in this presentation start by identifying only the table values of x for domain, and the table of values of y for the range. I will identify them as student one and student two from left to right. Student two on the right, confuses the increasing and decreasing intervals with the range of the function. Both of the students have difficulty not laughing during the presentation. These two student also identify the function has having one turn which only applies to polynomials. This is an exponential function that is constantly increasing, and therefore should also not have any decreasing intervals. Danny helps clarify that Jason was correct in his first statement that the function was increasing from negative infinity to infinity.
This is the second sample presentation that I am providing. In this presentation, both students were given the function y=-2(x-1)^2-3. I did not give many students a problem with a vertical stretch in them, but I had introduced it. These students do not refer to the vertical stretch in the analysis of this function. These students also referred to the domain and range from the table only and not from the graph of the function. This function is reflected across the x-axis which the students do not reference in the presentation. Skylar raises his hand to clarify the reflection at the end of the video. Any parabola has one increasing and one decreasing interval for each side of the u-shape. This pair of students state two increasing intervals and one decreasing interval which is incorrect. This function also has a maximum which is not stated.
This is a third sample of the Parent Function Transformation Presentations. This pair of students have the function y=(x + 1)^2 + 1. In this presentation, these two students confuse several characteristics about their function. They confuse domain and range with increasing and decreasing intervals. They analyze the x-intercept on the parent function instead of the new function that has been transformed. They are confused also about the degree and number of turns. In most of the presentations, I let students help with the questioning of the presenters, and students were also able to provide feedback to groups and reasoning for characteristics of their function. In this presentation, there was too much confusion with the vocabulary, so I made it a teachable moment. I went to the front to help question and work with them and all of the students in the class to present their function. I took advantage at this point to not only look at the difficulties that this pair of students were having, but also re-teach some of the vocabulary that was difficult for most groups.