Getting a function onto your TI-84 screen

To graph on a TI-84 Plus, you enter the function into the calculator, set the viewing window, and press Graph. The calculator plots points along the function and connects them with a line. Most graphing happens in the Y= editor, where you type the equation exactly as the calculator expects it.

Press the Y= button near the top left of the keypad. You will see a list starting with Y1=, Y2=, Y3=, and so on. The cursor sits next to Y1=. Type your function using X as the variable. For example, to graph y = 2x + 3, type 2X+3. Use the × button for multiplication and the ÷ button for division. The calculator reads what you type left to right, so parentheses matter: (2+3)X is different from 2+3X.

After you type the equation, press Enter. The equation stays in the Y1 slot and the cursor moves to Y2=. If you only want to graph one function, press Graph now. The calculator will display your function on the screen.

Key Takeaways

  • Press Y=, type your equation using X as the variable, and press Graph to see the result on screen.
  • The default window shows x from −10 to 10 and y from −10 to 10; use Zoom to fit the graph or Window to set your own range.
  • Parentheses control order of operations, so (X+1)^2 and X+1^2 produce different graphs.
  • You can graph up to ten functions at once by entering them in Y1 through Y0, and toggle each one on or off using the equals sign highlight.
  • Trace lets you move a cursor along the graph to read exact coordinates; use the arrow keys to move left and right.

Understanding the default window and when to change it

When you press Graph, the calculator uses a default window: x ranges from −10 to 10, and y ranges from −10 to 10. This works well for straightforward linear functions like y = x or y = 2x + 5. For other functions, the graph may be too zoomed in, too zoomed out, or centered in the wrong place.

The fastest fix is the Zoom menu. Press Zoom (above the Trace button). You will see options including ZoomFit, ZoomStandard, and ZoomBox. Press 0 for ZoomFit, and the calculator automatically adjusts the window so the entire function fits on screen. This works for most homework problems. If you want to zoom in on a specific region, select ZoomBox, use the arrow keys to draw a box around the area you want to see, and press Enter.

If you need exact control, press Window (to the left of Zoom). You will see fields for Xmin, Xmax, Ymin, Ymax, Xscl, and Yscl. Xmin and Xmax set the left and right edges of the graph; Ymin and Ymax set the bottom and top. Xscl and Yscl control the spacing of tick marks on the axes. For a parabola like y = x², try Xmin = −5, Xmax = 5, Ymin = −2, Ymax = 25. Type each value and press Enter to move to the next field. When you finish, press Graph.

Entering equations with exponents, fractions, and special functions

Exponents use the ^ button (Shift + 6). To graph y = x², type X^2. For y = x³, type X^3. For fractional exponents like y = x^(1/2), use parentheses: X^(1/2). Without the parentheses, the calculator reads X^1/2 as (X^1)/2, which is just X/2.

Square roots, cube roots, and other functions live in the Math menu. Press Math and scroll to find sqrt (square root), or press 2nd + x² for the square root symbol. To graph y = √x, press 2nd + x², then type X, then close the parenthesis. The screen shows √(X). Trigonometric functions like sin, cos, and tan are buttons on the keypad. To graph y = sin(x), type sin(X). Make sure your calculator is in the right mode: press Mode and check whether Radian or Degree is highlighted. Most calculus uses radians; most high school trigonometry uses degrees.

Absolute value uses the Math menu as well. Press Math, scroll right to NUM, and select abs. To graph y = |x − 2|, type abs(X−2). Logarithms and exponentials are on the keypad: log is base 10, ln is natural log, and e^X is found by pressing 2nd + ln.

Graphing multiple functions and turning them on and off

You can enter up to ten functions at once. After you type the first equation in Y1 and press Enter, the cursor moves to Y2=. Type a second equation and press Enter. Each equation appears in its own slot. Press Graph and both functions display on the same axes.

To turn a function off without deleting it, go back to Y= and highlight the equals sign in that row. Press Enter and the equals sign changes from solid to dotted. When you press Graph, the dotted equation does not appear. Press Enter again to turn it back on. This is useful when you want to compare two graphs side by side or focus on one function at a time.

The calculator assigns each function a different color or line style on newer models. If you graph Y1 = X and Y2 = X², you can see both curves and tell them apart. If the window is too crowded, use Zoom or Window to adjust, or turn off some functions temporarily.

Using Trace to read coordinates off the graph

After you press Graph, press Trace to set up the trace cursor. A small dot appears on one of your functions, and the coordinates show at the bottom of the screen. Use the left and right arrow keys to move the dot along the graph. The x and y values update as you move.

If you graphed multiple functions, press the up and down arrow keys to jump between them. This is useful for finding where two graphs intersect: trace along one function until you are close to the intersection, then press the up or down arrow to switch to the other function and see how close you are.

Trace shows only points the calculator actually computed. If you move the cursor and the coordinates jump, the calculator skipped some x values. This happens when the window is very wide or the function changes rapidly. Zoom in to see more detail, or use the Calc menu (2nd + Trace) to find exact values like intersections, maxima, and minima without tracing by hand.

Common mistakes and how to fix them

The most common error is forgetting parentheses around the argument of a function. If you type sin X instead of sin(X), the calculator reads it as (sin)(X), which is not what you want. Always use parentheses after function names like sin, cos, sqrt, and abs. Similarly, if you type 1/2X meaning (1/2)X, the calculator reads it as 1/(2X). Use parentheses: (1/2)X or 0.5X.

If your graph does not appear or looks wrong, check the Window settings first. Press Window and verify that Xmin is less than Xmax and Ymin is less than Ymax. If Ymin and Ymax are very close together, the graph will be stretched vertically and may look like a line. If they are very far apart, the graph will be compressed and may be hard to see. Use ZoomFit to let the calculator choose sensible values.

If you see only a blank screen, the function may be outside the current window. For example, if you graph y = 100x + 500 with the default window (y from −10 to 10), the line is far above the visible area. Press Zoom and select ZoomFit, or manually set Ymin to a negative number and Ymax to a large positive number.

Saving and clearing graphs

The TI-84 Plus does not save graphs themselves, but it does save the equations in the Y= editor. When you turn the calculator off and back on, your equations stay in Y1, Y2, and so on. If you want to start fresh, press Y=, highlight an equation, and press Delete. The equation disappears and the slot becomes empty.

If you want to clear all equations at once, press 2nd + Mode (which is the All-Reset option on some models), or manually delete each equation one by one. Some calculators have a ClrAllLists option in the Stat menu, but this clears data lists, not graphing equations.

To print or share a graph, you can take a photo of the screen or use a TI-Connect cable to transfer images to a computer. The calculator itself does not have a built-in print function.

Frequently Asked Questions

Why does my graph look like a straight line when it should be curved?

The window is probably too zoomed out. Press Zoom and select ZoomFit, or press Window and make Ymin and Ymax closer together so the curve takes up more of the screen. For example, if you graph y = x², the default window shows the parabola as a thin V shape. Set Ymin = 0 and Ymax = 25 to see the curve more clearly.

How do I graph a piecewise function like y = x if x < 0 and y = x² if x ≥ 0?

Use the test operators in the Math menu. In Y1, type X(X<0) + X^2(X≥0). The calculator treats true conditions as 1 and false as 0, so this expression evaluates to X when x is negative and X² when x is zero or positive. Press 2nd + Math to find the comparison operators like <, ≥, and =.

Can I graph an equation that is not solved for y, like x² + y² = 25?

You need to solve for y first. For x² + y² = 25, rearrange to y² = 25 − x², then y = ±√(25 − x²). Enter Y1 = √(25 − X²) and Y2 = −√(25 − X²). Both equations together form the circle. This works for any implicit equation as long as you can solve for y algebraically.

How do I find the exact intersection of two graphs?

Press 2nd + Trace to open the Calc menu. Select Intersect, and the calculator asks you to identify which two functions to find the intersection of. Use the arrow keys to highlight each function, press Enter for each, and the calculator shows the exact x and y coordinates where they meet.

What is the difference between Radian and Degree mode?

Radian mode treats angle inputs as radians (where 2π radians = 360 degrees). Degree mode treats them as degrees. If you graph y = sin(x) in Radian mode, the function completes one full cycle from x = 0 to x = 2π ≈ 6.28. In Degree mode, it completes one cycle from x = 0 to x = 360. Check your Mode setting before graphing trigonometric functions.