Reflect on the concept of function. What concepts (only the names) did you need to accommodate the concept of function in your mind? What is the simplest function you can imagine? In your day to day, is there any occurring fact that can be interpreted as a function? Is it possible to view a function? What strategy are you using to get the graph of a function?
Function is a fundamental concept in mathematics that describes the relationship between two sets of values, where each input value produces a unique output value (Abramson, 2021). In order to understand the concept of function, I needed to accommodate several related concepts in my mind, including domain, range, mapping, inverse, composition, and graphing.
The domain of a function refers to the set of all possible input values that can be used to produce an output value. The range, on the other hand, is the set of all possible output values that can be obtained from the function. Mapping is the process of assigning each input value to its corresponding output value. The inverse of a function is another function that reverses the mapping, allowing us to find the input value that produced a given output value. Composition is the process of combining two or more functions to create a new function (Abramson, 2021).
The simplest function I can imagine is f(x) = x, which is a linear function that maps each input value to itself. This function has a domain and range of all real numbers, and its graph is a straight line passing through the origin with a slope of 1.
In my day-to-day life, there are many occurrences that can be interpreted as functions. For example, the relationship between the amount of time I spend exercising and my level of physical fitness can be described as a function. Similarly, the relationship between the amount of money I spend on groceries and the quantity and quality of food I have available can also be described as a function.
While it is not possible to view a function directly, we can represent it graphically using a coordinate plane. The graph of a function shows how its input values are mapped to its output values, and allows us to visualize the relationship between them. To get the graph of a function, I typically start by identifying its domain and range, and then plot several points on the coordinate plane by choosing input values and calculating their corresponding output values. I then connect these points with a smooth curve to create the graph of the function. Alternatively, I can use software or a graphing calculator to generate the graph automatically.
To sum up, the concept of function is a fundamental and versatile tool in mathematics that allows us to describe and analyze relationships between sets of values. Understanding this concept requires grasping related concepts such as domain, range, mapping, inverse, composition, and graphing. Although we cannot view a function directly, we can represent it graphically using a coordinate plane. The simplest function is f(x) = x, which is a linear function mapping each input value to itself. In everyday life, many occurrences can be interpreted as functions, like the relationship between time spent exercising and physical fitness.
References
Abramson, J. (2021). Algebra and trigonometry (2nd ed.). OpenStax, TX: Rice University. Retrieved from https://openstax.org/details/books/algebra-and-trigonometry-2e