"During the function exercise today I learned new things and also was reminded of some I learned in Calculus last year. Through the activity my group and I remembered that to have a function the graph has to pass the vertical line test. We were sure to use this rule before drawing each segment. We also learned that a function does not have to be continuous, but that every x-value has to have a y-value that it coordinates with. Another idea that was brought to mind was that there are probably infinitely many graphs that could pass as a function. This exercise was helpful in reminding me of some of the basic rules of functions."
"My response to the activity that we did with the functions was how unpredictable functions are. Every prediction that we made about the function could have had an infinite amount of variations to it. It has been a year since my last math class and so I need to reivew all of the requirements of a function. The vertical line test was a review as was incontinuous functions."
"I am not a morning person. The mere thought of an 8:00 calculus class terrifies me. Not only do I have to wake up early, I have to be alert early. So I was extremely nervous about the first day of class. I feared I would not be able to talk or even think that early, let alone graph a function. However, all my worries waned as the class period passed. During the graphing exercise, my mind began to work, and I became more confident in my early--morning mathematical abilities. The hands-on activity woke my body and mind up, and the group setting forces me to interact with others, making me even more alert. The exercise reminded me of the basic concepts discusseed in Pre-Cal and Calculus at my high school. I was reminded that a function need not be continuous or even predictable. I began to remember the different mathematical terms that I had been so accustomed to hearing during the school year. Before I knew it, I had made the transition into a college calculus class."
"At first I felt like I had forgotten EVERYTHING about Pre-Cal and Calculus. Then after the first set of graphs I was beginning to remember some of what I learned. Some of the graphs really surprised me."
"Having an extremely weak background in calculus, I was surprised at the outcomes of the graphs. It made me think, probably for the first time, about how it would be possible to write an equation for such graphs. The discontinuity and reversal of slope direction exhibited in the functions challenged me to think of different ways of looking at them."
"It's easy to forget that there's not only one solution for everything. In calculus, there are infinite possibilities and infinite ways a graph can look. Also, there are no wrong answers."
"In discussing the problems with the other group members, I was reminded of terms which I haven't dealt with in a couple of years. ... such as bound functions, as well as the idea behind the vertical line test for relevancy of a function. It was a good exercise to refresh my memory as well as get me back into the 'math' sense of mind."
"The concepts you presented today were easy to understand and I like the way you did not assume that everyone knew what some simple concepts were: like functions."
"...Most students would prefer their graphs to look like parabolas and sin/cos waves. A smooth graph appeals to the eye more than an haphazard scattering of points; however, not all graphs can be aesthetically pleasing. We must learn to accept graphs for their mathematical functions and save our aestheticism for a trip to the beach."