How to View Discontinuities on Desmos
Discontinuities are an essential concept in calculus and analysis, representing points where a function is not continuous. They can be classified into different types, such as jump discontinuities, infinite discontinuities, and oscillating discontinuities. Desmos, a powerful graphing calculator, allows users to visualize and understand these discontinuities effectively. In this article, we will discuss how to view discontinuities on Desmos and explore various examples to enhance your understanding.
1. Accessing Desmos
To begin, you need to access Desmos. You can either visit the Desmos website or download the Desmos app on your smartphone or tablet. Once you have Desmos open, you can start creating graphs and exploring functions.
2. Entering the Function
In the input field, enter the function you want to analyze. For example, let’s consider the function f(x) = (x^2 – 1) / (x – 1). This function has a discontinuity at x = 1, as the denominator becomes zero, making the function undefined at that point.
3. Plotting the Function
After entering the function, Desmos will automatically plot the graph. The graph will show the function’s behavior on the selected interval. In our example, you will notice a gap or a hole at x = 1, indicating the discontinuity.
4. Adjusting the Graph
To get a better view of the discontinuity, you can adjust the graph’s settings. Click on the “Graph” button in the menu bar and select “Range.” You can then input the interval you want to focus on, such as (-10, 10) or (-5, 5), depending on the function and the discontinuity’s location.
5. Analyzing the Discontinuity
Now that you have the graph adjusted, you can analyze the discontinuity. In our example, the discontinuity at x = 1 is a removable discontinuity. To understand this, you can simplify the function by canceling out the common factor (x – 1) in the numerator and denominator:
f(x) = (x^2 – 1) / (x – 1) = (x + 1)(x – 1) / (x – 1) = x + 1
As you can see, the simplified function is f(x) = x + 1, which is continuous at x = 1. This means that the discontinuity in the original function can be “removed” by canceling out the common factor.
6. Exploring Other Types of Discontinuities
Desmos can also help you visualize other types of discontinuities, such as jump discontinuities and infinite discontinuities. To explore these, you can try functions like f(x) = 1 / (x – 2) and f(x) = 1 / x, respectively. By adjusting the graph’s settings and analyzing the behavior of the function, you can gain a deeper understanding of these discontinuities.
In conclusion, Desmos is an excellent tool for visualizing and understanding discontinuities in functions. By following the steps outlined in this article, you can easily view and analyze different types of discontinuities, enhancing your knowledge of calculus and analysis.
