How to enter and graph a function on your TI-84 Plus
To graph a function on a TI-84 Plus, press the Y= button at the top left of the calculator, type your equation using the X variable, then press GRAPH. The calculator will display the curve on its screen. For example, to graph y = 2x + 3, you would press Y=, type 2X+3, and press GRAPH. The window will show the function plotted across a default range of x-values from −10 to 10.
The Y= screen holds up to ten different functions at once, labeled Y1 through Y0. Each function appears in a different color on the graph. You can enter multiple equations and see them all plotted together, which is useful for comparing functions or finding where they intersect.
If your graph looks wrong or appears blank, the issue is usually the window settings. Press WINDOW to see the range of x and y values the calculator is displaying. If your function should show values between −5 and 5 but the window is set to −100 to 100, you will see only a flat line or nothing at all. Adjust Xmin, Xmax, Ymin, and Ymax to match the range where your function actually appears.
Key Takeaways
- Press Y=, enter your equation using X as the variable, then press GRAPH to see the function plotted on the screen.
- You can enter up to ten functions at once in the Y= menu, and each will display in a different color on the same graph.
- If your graph appears blank or wrong, press WINDOW and adjust Xmin, Xmax, Ymin, and Ymax to show the correct range of values.
- Use ZOOM to quickly fit the graph to the screen or zoom in and out on specific regions without manually changing window settings.
- The TRACE button lets you move a cursor along the plotted function to read exact x and y coordinates at any point.
Adjusting the window to see your function
The window settings control which portion of the coordinate plane the calculator displays. By default, the TI-84 Plus shows x-values from −10 to 10 and y-values from −10 to 10. If your function has a steep slope or very large or very small values, you need to widen or narrow the window.
Press WINDOW to open the settings. You will see six values: Xmin (the leftmost x-value shown), Xmax (the rightmost), Ymin (the bottom), Ymax (the top), Xscl (the spacing of tick marks on the x-axis), and Yscl (the spacing on the y-axis). Change any of these by moving the cursor to that line, pressing DELETE to clear it, typing a new number, and pressing ENTER. After you change the window, press GRAPH to redraw with the new settings.
A faster way to fit your function to the screen is to press ZOOM and select option 0 (ZoomFit). The calculator will automatically adjust the window so the entire function is visible. You can also press ZOOM 6 (ZStandard) to reset to the default −10 to 10 window, or ZOOM 3 (Zoom Out) to see a wider area.
Using TRACE to read coordinates on the graph
Once your function is graphed, press TRACE to activate the trace cursor. A small square will appear on the function, and the x and y coordinates will display at the bottom of the screen. Use the left and right arrow keys to move the cursor along the function. As you move, the coordinates update in real time, letting you read the exact y-value for any x-value on the curve.
If you have multiple functions graphed, pressing the up and down arrow keys while in trace mode switches between them. This is useful for finding where two functions intersect: trace along one function until you reach the intersection point, then switch to the other function and verify they meet at the same coordinates.
The trace cursor only moves to points the calculator has actually plotted, so it jumps in small steps rather than moving smoothly. If you want to find a coordinate that falls between plotted points, you can manually enter an x-value while in trace mode by typing the number and pressing ENTER. The cursor will jump to that x-value on the current function.
Graphing more than one function at a time
Enter each function in its own line in the Y= menu. For example, to graph y = x², y = 2x, and y = x + 1 together, press Y=, type X^2 in Y1, press ENTER, type 2X in Y2, press ENTER, and type X+1 in Y3. Then press GRAPH. All three functions will appear on the same coordinate plane in different colors.
You can turn individual functions on and off without deleting them. In the Y= menu, move the cursor to the equals sign of the function you want to hide, and press ENTER. The equals sign will change appearance (usually becoming unselected or highlighted differently), and that function will no longer appear on the graph. Press ENTER again to turn it back on. This is helpful when you want to focus on one or two functions without clearing the others.
Each function can have its own line style. In the Y= menu, move to the left of the equals sign (where you see a diagonal line or other symbol), and press ENTER to cycle through different styles: solid, thick, dotted, or animated. Changing the style helps distinguish functions that are close together or hard to tell apart by color alone.
Finding intersections and key points
To find where two functions cross, graph both of them, then press 2ND and TRACE (which opens the CALC menu). Select option 5 (Intersect). The calculator will ask you to select the first function, the second function, and a guess for where they meet. Use the arrow keys to move the cursor near the intersection point and press ENTER three times. The calculator will display the exact x and y coordinates where the functions intersect.
The CALC menu also has other useful tools. Option 2 (Zero) finds where a function crosses the x-axis. Option 3 (Minimum) and option 4 (Maximum) find the lowest and highest points on a function within a given range. Option 1 (Value) lets you type in an x-value and see the corresponding y-value without using trace mode.
For each of these operations, the calculator asks you to provide a guess or a range. Move the cursor close to the feature you are looking for (the zero, minimum, maximum, or intersection) and press ENTER. The calculator will then refine the position and display the result. This is much faster and more accurate than trying to read coordinates by eye from the graph.
Clearing functions and resetting the calculator
To delete a single function from the Y= menu, move the cursor to that line and press DELETE. The entire equation will be erased, and the line will become blank. You can then enter a new function in that space, or leave it blank.
To clear all functions at once, press Y=, then press 2ND and DEL (which is the minus button). Select option 1 (ClrAllLists) or manually delete each line. If you want to reset the window to the default −10 to 10 view, press ZOOM and select option 6 (ZStandard).
If the calculator is behaving strangely or you want to start fresh, you can reset it. Press 2ND and + (the plus button, which is MEM), select option 7 (Reset), and choose option 1 (All RAM). This will clear all functions, window settings, and stored values, returning the calculator to its factory state. You will lose any custom settings or saved data, so only do this if you are sure you want to start over.
Frequently Asked Questions
Why does my graph show only a blank screen or a flat line?
The window settings are almost always the problem. Press WINDOW and check that Xmin is less than Xmax and Ymin is less than Ymax. If your function has large y-values (like y = x² at x = 100), but Ymax is only 10, you will see nothing. Press ZOOM 0 (ZoomFit) to let the calculator choose appropriate window settings automatically.
How do I graph an inequality like y > 2x + 1?
The TI-84 Plus can shade regions for inequalities, but it requires a different approach than graphing a simple function. In the Y= menu, move to the left of the equals sign and press ENTER to cycle through shading options (the symbol will change from a line to a shaded pattern). Then enter the boundary equation. The calculator will shade the region above or below the line depending on which shading style you select.
Can I graph a circle or other shape that is not a function?
Yes, but you need to enter it as two separate functions. A circle with equation x² + y² = 25 can be split into y = √(25 − x²) and y = −√(25 − x²). Enter both in the Y= menu and graph them together. The two halves will form a complete circle. For other non-function shapes, you may need to use parametric or polar graphing modes, which are accessed through the MODE menu.
How do I save a graph or print it?
The TI-84 Plus does not have a built-in print function, but you can take a photo of the screen with a phone or camera. Some graphing software and computer programs can connect to the calculator via a USB cable to transfer and save graphs, but this requires additional software and hardware. For most purposes, sketching the graph on paper while looking at the screen is the simplest approach.