loading...loading...Desmos is a web-based graphing calculator that allows you to plot points, graph expressions, and evaluate equations. It is a versatile tool that can be used to visualize mathematical concepts and solve problems. This guide will introduce you to the basics of using Desmos and help you get started with graphing points and curves.
The expression list is located on the left side of the graphing calculator and is Desmos' way of storing your wonderful math. You can add an expression by clicking on the gray plus sign in the top left and selecting "expression."
An expression could be a calculation, a variable, a function ... just to name a few. You can type math on your keyboard or using the built-in Desmos keypad in the bottom left. Try typing something like \(2 + 3\) or \(\cos(\pi)\) in a new expression line.
You can delete an expression by clicking on the gray \(\times\) or pressing backspace on an empty line. You can undo actions by pressing Ctrl/Cmd + Z or the undo button, or redo them by pressing Ctrl/Cmd + Shift + Z or the redo button.
Unlike traditional graphing calculators, Desmos updates the graph in real time as you type your expressions. This means you can see the effects of your changes immediately.
In the expression list, try plotting a point like \((1, 3)\), graphing a line like \(y = -2x + 4\), or graphing a parabola like \(y = x^2 - 1\). You can toggle the graph of an expression by clicking its colored icon on the left side of the expression list.
Whenever you add a free variable (practically any character except \(x, y, e,\) or \(\theta\)) to your equation, Desmos gives you the option to define it as a slider. Sliders are a great way to visualize how changing a variable affects the graph. Try dragging the \(a\) slider until the line \(y=ax\) intersects the red point.
To set the bounds of the slider, click on either of the values at the ends of the slider ends and enter your desired upper/lower bounds. You can change the "step" value to adjust the increment of the slider. By default, the slider moves continuously. You can also use the play button next to the slider to automatically cycle through all of the slider values. Directly below the play button, you can access the animation properties to change the animation mode and speed.
You can define your own functions in the expression list, such as \(f(x)\) or \(g(x)\), which can be used in other expressions. For example, you can create a function \(f(x) = x^3\) and then graph \(y = f(x) + 5\) to see the graph of \(f(x)\) translated up 5 units. You can also use functions to evaluate expressions at specific inputs, such as \(f(3)\).
To see points of interest (\(x\) and \(y\)-intercepts, intersections, local minimums/maximums, etc.), select the curve you're interested in on the graph, and hover over or click the gray points to see their coordinates.
Desmos can be used to visualize both explicit and implicit inequalities, resulting in colored shading above, below, or within lines and curves.
Strict (non-inclusive) inequalities, represented by dashed lines on the graph, can be created using the \(<\) and \(>\) symbols in place of the typical equals sign. Non-strict (inclusive) inequalities, represented by solid lines on the graph, can be created using the \(\leq\) or \(\geq\) symbols.
Solutions to multiple inequalities are shaded in both colours, as shown by the overlapping red and blue region in the top right of the graph.
To add domain or range restrictions, use curly brackets at the end of an expression, as shown in the expression list. You can restrict \(x\) or \(y\) values, or any input variable you specify for a function.
Adding multiple restrictions for the same expression is a little tricky. For "either/or" restrictions, you can separate each variable restriction with a comma, all within the same pair of curly brackets. This restriction displays regions that satisfy either of those inequalities.
For "both/and" restrictions, put each variable restriction in a different pair of curly brackets. This restriction displays regions that satisfy both of those inequalities.
Let's take the graph as an example. The restriction on the blue expression, \(\{x>0, y < 4 \}\), looks for regions where either \(x>0\), \(y < 4\), or both. The restrictions on the green expression, \(\{x<-1 \}\{y>5 \}\), look for regions where both \(x<-1\) and \(y>5\).
The graph settings menu can be opened using the wrench icon in the upper right corner and, as the name suggests, is ideal for changing the properties of the graph. For example, if you want to view a certain area of the graph, you can open the menu and enter a lower and upper limit for the \(x\) and \(y\)-axes.
From the graph settings menu, you can also enlarge the graph display, hide or reduce the density of gridlines, switch between Cartesian and polar coordinates, create labels for your axes, and switch between radians and degrees. From the "More Options" drop-down, you can enable logarithmic scaling and lock the viewport to prevent the current view from being changed.
Use the "More Options" drop-down in the graph settings menu to enable logarithmic scaling for both axes. Then change the bounds for the \(x\)-axis to \(1\leq x \leq 10^4\) and the bounds for the \(y\)-axis to \(10^4 \leq y \leq 10^{10}\) to see a secret message!
It looks like someone left this graph in pretty bad shape.... For starters, it is way too zoomed in! To move around the coordinate grid, you can click and drag the graph. You can zoom in and out by scrolling or using the \(+\) or \(-\) buttons in the upper right. To return to the default view, press the home button below.
It looks like this is supposed to be a smiley face, but it's not quite right. Try moving the \(a\) slider to put the left eye back in place. Finally, change the bounds of the parabola to bring back the left half of the smile!
If you're feeling creative, consider adding a feature to the smiley by graphing an expression of your own. You can customize the visual style (line width, opacity, color, etc.) of a graphed expression by holding down on its colored icon on the left side of the expression list.
Looking for inspiration? Check out the Desmos 2024 Art Expo!