1. Reflect on the concept of composite and inverse functions. What concepts (only the names) did you need to accommodate these concepts in your mind?
composite functions
composition
the input value (Abramson, 2017)
the output value (Abramson, 2017)
the inside function
the outside function
inverse function
domain
co-domain
range
the inverse
the identity function,
row (Abramson, 2017)
column (Abramson, 2017)
reflection
the diagonal line
the identity line
the horizontal extent (Abramson, 2017)
the vertical extent (Abramson, 2017)
mirror line
2. What are the simplest composite and inverse functions you can imagine? In your day to day, is there any occurring fact that can be interpreted as composite and inverse functions?
A compound function is a function that combines two separate functions such that the output of one function is chained as the input to the subsequent function (Abramson, 2017). For example, when printing a book, if we know the number of characters, the size of the characters, and the size of the paper, we can calculate the number of pages required to print all the text. We can also calculate the weight of the entire book by adding the weight of the paper to be printed. As another example, we assume that the higher the altitude, the lower the temperature; if we know the altitude of the mountain, we can calculate the approximate temperature difference from the ground. In addition, fuel economy can also be calculated from the car's weight and speed and the engine's performance.
An inverse function is a function obtained by exchanging the positions of x and y and looking at the same correspondence from the opposite direction, often used in the engineering field (Abramson, 2017). As the simplest example, assuming the candy you want to buy is 70 cents each, the cost of y cents to buy x candy is expressed as y=70x. Conversely, when I consider "I have (x) cents now, and how many candies (y) can I buy," the number of candies available for purchase is represented by y=x/70. At this time, y=70x and y=x/70 are inverse functions of each other.
4. What strategy are you using to get the graph of composite and inverse functions?
When I was a student, I created graphs of composite and inverse functions by substituting various values into functions to obtain coordinates and connecting the marked coordinates with lines. Currently, I am creating graphs using the Desmos site, which is recommended for use in courses. If you enter a function, the graph will be created automatically. It is also possible to draw multiple graphs in one table, which is very convenient for color-coding and comparing. It is easy and comfortable, but I miss my student days a little.
Thank you professor. (450 words)
Reference
Abramson, J. (2017). Algebra and trigonometry. Opens tax, TX: Rice University. Retrieved from https://openstax.org/details/books/algebra-and-trigonometry
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