Math allows us to break up the world into little abstract pieces so that it’s easier to understand. By doing this, we can study specific parts of the world in isolation, uncovering their properties on both a microcosmic and macrocosmic level.
Calculators are one tool that many people use to enhance their study of math. Function calculators are especially helpful, as they allow you to input functions on the calculator and receive all kinds of output information.
In this article, we discuss function calculators in more depth, giving a brief overview of them and emphasizing their benefits and drawbacks. Then, we give a step-by-step guide on how to use a function calculator, ending with our thoughts on the future of function calculators.
AN OVERVIEW OF FUNCTION CALCULATORS
Function calculators are just a specific type of calculator that anyone interested in math can benefit from.
Most commonly, students use function calculators when they are learning about various functions, though professors also use them both to teach and to do research.
Some of the most advanced graphing calculators, like the TI-84 Plus CE, have color graphing applications that allow the user to enter in multiple functions and view the graphs of these.
Some graphing calculators will set limits on how many functions you can graph as well how many variables are allowed in the graphed function and what information is displayed on the graph. The most advanced graphing calculators will even allow you to graph functions of 3 variables or more. These are usually found online, like the one offered by GeoGebra.
Thus, in one sense, function calculators are really the same thing as graphing calculators. Function calculators just emphasize the analysis of functions and provide information that students usually seek from functions. This includes determining x and y-intercepts, max and min values, the domain and range, vertex values, and many other outputs.
The most effective function calculators will allow you to customize what information is displayed once you input a function. The most basic function calculators, on the other hand, will only allow you to input the simplest of graphs, usually with no more than two variables.
Two of the most popular online function calculators are offered by Symbolab and Desmos. Most online function calculators will also offer you other tools to enhance your math education, so make sure you have the function calculator option selected before you begin your work.
THE BENEFITS OF FUNCTION CALCULATORS
Function calculators usually work by allowing users to enter a function to analyze. Some function calculators allow users to enter in output information first in order to determine what function(s) would yield this information. Regardless, function calculators are designed to shine a spotlight on some function you’ve been considering.
Functions are important in disciplines other than math, most specifically physics and engineering. They are condensed containers of information. Like a human being, each function is totally unique yet shares qualities with other functions.
Modern math students are constantly standing on the shoulders of giants, relying on the knowledge uncovered by past mathematicians in order to push the subject forward. The explorations of many famous mathematicians have led to many modern theories and shortcuts that allow us to compute values faster than ever before. Thus, function calculators allow us to expedite our learning and benefit from the discoveries of past titans in the field.
Without a function calculator, we would have to graph each function by hand as well as manually calculate important values. While this might be tolerable at first, eventually this practice would become impractical, especially as you moved on to the higher math classes. In some advanced classes, not only is a function calculator helpful, it’s actually a necessity.
What’s really great about modern function calculators is their ability to be accessed online. This truly levels the playing field when it comes to math education, allowing anyone with an internet connection to graph and analyze complex functions. Some function calculators will even allow you to download them so they can be used offline.
Some students who would usually not be inspired by math topics are surprised to find themselves not only enjoying the subject but considering a career in it. Function calculators are especially helpful for these students who want to explore a topic in more depth. Many beginner students are fascinated by how space and extension relate to abstraction, making function calculators which deliver sharp, colorful graphs an indispensable tool throughout their educational process.
THE BENEFITS OF CUSTOMIZABLE FUNCTION CALCULATORS
Some of the most advanced function calculators will allow you to customize what information is displayed upon entering a function.
This is especially useful for more advanced students who are studying a certain function. This happens frequently in graduate school, as many students zero in on a segment of math that they are interested in, focusing on analyzing some shape or structure that can be described using the language of functions.
These students would benefit from a function calculator that can be modified to display information relevant to their research. Some graduate students need to compute large amounts of data concerning many types of similar functions. In order to avoid spending countless hours doing this by hand, these students elect to use an online function calculator that can be personalized. This makes their work more efficient.
THE DRAWBACK OF FUNCTION CALCULATORS
The main drawback of function calculators is that they can lead to you relying on a calculator in order to remember the properties of a function.
Learning the properties of many functions is important if you want to continue studying math in the future. Many higher-level math classes will require you to know the properties of some functions in order to enroll. Graphing some of the most popular functions by hand and probing their properties can be a great way to keep your skills up to date.
Like a used car, your mathematical mind must be occasionally oiled and tuned up to facilitate optimal performance. Constantly using a function calculator is like procrastinating when it comes to taking the car in to get an oil change or check-up. You might be able to get by for a bit longer, but one day your laziness might come back to haunt you.
A Step-by-Step Guide of How to Use a Function Calculator
Using a function calculator can be very easy as long as you are able to recognize what information to enter and where to enter it. Most online function calculators will give an initial blank asking for you to type in a function. When you type in the function, make sure you copy it down verbatim, using any special characters or symbols that might be necessary.
More complicated functions might involve going to specialized websites. If a certain online calculator can’t analyze a function with a certain character, then try googling the function and seeing what search results you get.
After you’ve found an online website and correctly entered the function, hit “go” or “graph”. Some online function calculators will simply require you hit the return key. After you do this, a graph of your function should appear as well as any data that you requested.
Some function calculators will offer to show you the work required to calculate certain function values. Sometimes you have to select the “show” option in order to access this feature. This is especially helpful for students who are just being exposed to a function for the first time.
Lastly, many function calculators will allow you to store functions that you might want to use in the future. This can be helpful if you want to compare many functions but don’t want to re-enter each one every time. Many function calculators will have helpful features like this that can only be discovered by experimenting with them.
OUR FINAL THOUGHTS ON FUNCTION CALCULATORS
We think the future of function calculators will be truly radical.
We see function calculators as being valorized not only as tools in the future but also as legitimate teachers. We mean this on both a metaphorical and literal level. We see math students of the future using virtual reality headsets in order to engage with numbers and functions on a more personal level.
We can envision a future in which students graph a function and then are able to enter the world of the graph, climbing on curves like mountains and walking along lines like a trail. Why learn from a professor when you can learn from the numbers or functions directly?
In this sense, we see the future of function calculators as coinciding with the future of technology. As technology changes, so will the tools available for us to study math.
In fact, future technology could be so powerful that modern function calculators become obsolete. Perhaps future function calculators will not require the use of some external hardware but will instead be integrated into our neurochemistry, allowing our brains to transform into function calculators literally in the blink of an eye,
Whatever happens, we think it will be truly revolutionary.