How to do absolute value on Desmos?

Desmos is a powerful graphing tool that allows users to visualize functions and equations in real-time. One common function that users may want to graph is absolute value. Absolute value represents the distance of a number from zero on the number line, so it is always positive. Here’s how you can easily graph absolute value functions on Desmos:

1. **Open the Desmos graphing calculator:**

First, go to the Desmos website or open the Desmos app on your device.

2. **Enter the absolute value function:**

To graph an absolute value function, you can simply use the absolute value notation, “| |”. For example, to graph the absolute value of x, type in “|x|”.

3. **View the graph:**

Once you enter the absolute value function, Desmos will automatically generate the graph for you. You can zoom in, zoom out, and move the graph around to explore different parts of the function.

4. **Customize the graph:**

If you want to customize the appearance of the graph, you can change the color, line style, and other settings using the options available in Desmos.

5. **Explore other absolute value functions:**

You can experiment with different absolute value functions by replacing the variable inside the absolute value notation. For example, you can graph “|2x|” or “|3x+4|”.

6. **Save and share your graph:**

Once you have created the graph of the absolute value function, you can save it to your Desmos account or share it with others by copying the link.

7. **Use sliders for interactive graphs:**

To make your graph interactive, you can add sliders to the absolute value function. This allows you to dynamically change the value of a variable and see how it affects the graph.

8. **Combine absolute value functions with other functions:**

You can combine absolute value functions with other functions on Desmos to create complex graphs. For example, you can graph “|x| + 2” to see how adding a constant affects the graph.

9. **Trace the graph:**

To trace the graph of the absolute value function, you can click on the curve and drag your cursor along the curve to see the coordinates of different points.

10. **Find the vertex of the graph:**

The vertex of an absolute value function is the point where the graph changes direction. You can find the vertex by looking at the lowest point on the graph if the coefficient of x is positive, or the highest point if the coefficient is negative.

11. **Check for symmetry:**

Absolute value functions are symmetric about the y-axis. You can check for symmetry by folding the graph along the y-axis and seeing if the two halves match.

12. **Graph piecewise absolute value functions:**

If you want to graph a piecewise absolute value function, you can use the piecewise notation in Desmos. For example, you can graph “f(x) = {x, x ≥ 0 | -x, x < 0}" to create a piecewise absolute value function. By following these simple steps, you can easily graph absolute value functions on Desmos and explore the properties of these functions visually. Desmos provides a user-friendly interface that makes it easy to create and manipulate graphs, making it a valuable tool for students, teachers, and math enthusiasts alike.

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