Lesson Objective: Find the domain and range of a function from its graph.
We have learned that certain relationships between two variables are called functions. If a relationship is a function, then for every input 
there is only one output 
.
The domain is the set of all possible values of for a function. It is a set so we use set notation such as 
.
The range is the set of all possible values of for a function. It is also a set so we use set notation such as 
.
Example 1:
Find the domain and range of the function with the following graph.
Domain:
Range:
Example 2
Domain:
Range:
Example 3
Domain:
Range:
Example 4
Domain:
Range:
Video
Question #2 on Page 387
When I first started thinking about this assignment, I thought of topics that my students have struggled with in the past and Domain and Range topped my list. It is a difficult concept that diagrams in textbooks just don’t explain effectively. To enhance student learning, rather than relying on text and diagrams, I drew graphs of the function and domain/range on Desmos and used the animate feature with some Math tricks to show how the domain can be visualized. In addition to creating graphics using screenshots, I used GIPHY Capture to create short gifs for the lesson so the students can repeatedly watch the process. The minimal use of text is intentional so that students can try to develop understanding through visuals but I also added a video with explanations for students who need further support. To create the video, I used the screen recording feature in Quicktime, then used Handbrake to reduce the video file size from 113.3MB (.mov) to 7.2MB (.mp4). Finally, I uploaded the video to YouTube and embedded the video in the lesson. Quick LaTeX was used for all the Mathematical formulas.
The font used is Libre Franklin (a sans-serif font) for ease of reading and there is high contrast between the font and background colors for better comprehension and reading speed. Headers and lists with hyperlinks to anchors on the page are also used as organization tools (Webster, 2014). Domain and Range is a deep topic but this lesson focuses on one small chunk without extraneous elements in accordance to Cognitive Load Theory (Webster, 2010). I used interpretive graphics (Clark and Lyons, 2010) to show the relationship between the graph of the function and its domain and range. The gifs are provided so that students can learn at their own pace and watch an example over and over again until they understand, based on the Segmenting Principle (Mayer, 2014). The positioning of the diagrams, such as the static domain image shown directly below and the static range image shown directly to the right of the animation as well as the positions of the equations for the domain and range, are based on the Spacial Contiguity Principle (Mayer, 2014). I used narration for the video with no words on screen to avoid split attention and overloading the visual channel as prescribed by the Modality Principle (Mayer, 2014).
References
Webster, K.S. (2014). Text Design for Online Learning. Retrieved from
http://courses.olblogs.tru.ca/eddl5131-jan17/week-2-text/text-design-for-online-learning/
Webster, K.S. (2010). Graphics for Learning. Retrieved from
http://www.youtube.com/watch?v=K5yd_M2xe78
Clark, R.C & Lyons, C. (2010). Three views of instructional visuals, In Graphics for Learning: Proven Guidelines for Planning, Designing and Evaluating Visuals in Training Materials. San Francisco: Pfeiffer, 15-28. Retrieved from
http://site.ebrary.com.ezproxy.tru.ca/lib/trulibrary/reader.action?
Mayer, R.E. (2014). Research Based Principles for Multimedia Learning.
Presentation given at Harvard University, 5 May 2014. Retrieved from
https://www.youtube.com/watch?v=AJ3wSf-ccXo
Hi Kaz,
I agree, domain and range seem to be really tricky for students. I often have high school kids that I taught in grade 9 come back to me for help and it’s always a challenge to help them grasp the concept. Desmos is awesome and it’s a great resource for students and teachers alike. I really like how you created gifs from the graph’s you created, I have never used GIPHY Capture so I will have to check that out. You ran into the same problem that I did in that you can’t pause a GIF. I also really liked the video. I’m going to bookmark it and if it’s ok with you I may share it with the next student that comes and asks for help with this topic. Lastly, if you’re looking for a cool assignment you can do with domain and range, one of my colleagues gets her students to use DESMOS to create line drawings that require domain and range. Here is a link to some examples on DESMOS: https://www.desmos.com/art
Abbi
Hi Abbi,
Thank you for the comment. Yes, the GIFs can’t be paused but I guess if they are short enough in duration, then it won’t pose a problem.
Please feel free to use the video – I’d be honored!
I checked out the line art done on Desmos – pretty impressive what people can do with graphs! I will set this as an assignment and I’m sure students will go crazy with it.
On the topic of Desmos, have you tried https://teacher.desmos.com? It is awesome! You find and set a task, which are like labs for the students, share a class code and then you can watch and track the progress of each student. Another one to check out if you have the time. Cheers.
Kaz,
I just checked out https://teacher.desmos.com/ and it’s fantastic. I remember looking at it once before but then got put on my “Do More With it Later Plate”. I have definitely bumped it up to my “Do Sooner Rather Than Later Plate” 🙂
Abbi
Hi Kaz,
I am impressed with the graphics and video! You are right when you say that students often struggle with domain and range. It doesn’t seem that difficult and yet students have a difficult time with the terminology and symbols. Probably because it is math! I will have to take a look at Desmos as well. Is there a way you could start the GIF right at the first point? For example, when x > -3, could the line start right at -3? This may help with the understanding. Great use of multimedia and visuals.
Markku
Hi Markku,
Yes, Domain and Range is easy if you know what to look for but it might not make any sense to a student who looks at it and become afraid. Thanks for the feedback about starting the GIF at the start of the domain to make it clear. I’ll give that a go on my next round.