Starting Spring 2024 semester. The little man is back!

I just noticed this draft has been siting here for days: It's been a few weeks since we returned to campus, and I'm still in the process of learning my students' names. However, the joy of being back, interacting with both students and colleagues, has brought a sense of home that energizes me, making me temporarily forget life's challenges. As an introvert-extrovert, diving into teaching allows me to explore my more outgoing side. This semester, I find myself solely focused on teaching precalculus, thanks to a teaching release that provides me with additional time. With this newfound time, I'm aiming to finalize some pending manuscripts. In these initial weeks, I've managed to learn several students' names and have already encouraged them to break the ice with each other. We've formed little teams to discuss precalculus problems collaboratively. Our topics have ranged from real numbers, understanding functions, and exploring graphs, to delving into domains, ranges, and transformations of basic functions. Our most recent discussion involved the composition of functions. During our exploration of functions, I revisited the analogy of the little man walking on the x and y-axes. The students chuckled, and I acknowledged that many find this visualization helpful when grasping domain and range from a graph. So, the little man has made a comeback to aid in understanding the intricacies of functions. I introduced the online graphing calculator, Desmos, and we dived into various graphs, exploring the tool's capabilities. Students were able to locate coordinates for x and y-intercepts, extract tables with values, and identify local extrema. As we progressed, we began experimenting with applying horizontal and vertical transformations to graphs from what I playfully referred to as the "alphabet of graphs." In contemplating future lessons, I'm considering the creation of a fun animation featuring the little man to visually explain the determination of the domain and range of graphs. Should I?