Reflection: Problem-based Approaches Domain and Range - Section 2: Whole Group Discussion + Practice

 

My students have the most difficulty identifying domain and range from a graph, especially when the end behavior approaches +/- infinity. The use of Desmos is crucial for helping students understand what is means for a function to not end, and that every function is bigger than what is on the 10x10 window on their papers. 

For example, y = 3x + 1, what is the output when we input 3 for x? What if we input 3000 for x? What if we input -0.000056 for x? Are we even able to do that? Are there any rules in math that limit the value of the number that is inputted?....This line of questioning should go on with very large and small numbers, so that students can understand why it is said that functions extend endlessy in both directions.

My students also have difficulty identifying the appropriate domain and range for a real world scenario with a finite beginning and/or end. To help students answer these types of questions, I support each problem with an input/output table. Students are then able to see which numbers are "allowed" in the table given the situation. Example, "number of cats vs. legs", will ONLY have multiples of 4 in its range. Also, the range can never be negative, as there is no such thing as a negative number of cats. To further extend, If I tell students that the input output table is for a room that contains 10 cats, the realization has to be made that the highest number for the range will be 40. If I wanted to plot this table, it would be a discrete function, because 1.5 cats does not exist.

  Domain and Range
  Problem-based Approaches: Domain and Range
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Domain and Range

Unit 2: Linear & Absolute Value Functions
Lesson 2 of 10

Objective: SWBAT identify the domain and range of a function. SWBAT analyze the domain and range of continuous and discrete functions.

Big Idea: Students will use real world examples to solidify their understanding of continuous and discrete inputs and outputs.

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