How to Graph Functions on TI-84 Calculator (Complete Guide)

How to Graph Functions on TI-84 Calculator (Complete Guide) The TI-84 graphing calculator is a powerful tool that can transform the way you understand and interact with mathematical functions. Whether you’re a student in algebra, calculus, or statistics, the ability to visualize equations is crucial. This comprehensive guide will walk you through every step of graphing functions on your TI-84, from basic lines to advanced parametric equations, with clear instructions and practical examples.

1. Getting Started: Know Your Calculator

Before you begin, familiarize yourself with the key buttons you’ll use for graphing:

Y= (Top Left): The most important button. This is where you enter the functions you want to graph.
WINDOW: This button allows you to define the portion of the coordinate plane you want to see (the X and Y boundaries).
ZOOM: This provides quick presets for your window, such as a standard -10 to 10 view or a view that fits all your functions.
TRACE: Lets you move a cursor along the graph to see the coordinates of points.
CALC (2nd + TRACE): A powerful menu for finding specific points on your graph, like intercepts, intersections, and slopes.
MODE: Ensure you are in the correct mode (e.g., “Func” for function graphing, “Rad” for radians in trigonometry).

How to Graph Functions on TI-84 Calculator (Complete Guide)

2. Step 1: Entering Your Functions (The Y= Editor)

Press the Y= button to access the function editor. You will see a list of potential functions, labeled Y₁, Y₂, Y₃, etc.

To enter a function:

Use the arrow keys to navigate to the function slot you want to use (e.g., Y₁).
Type your function using the X,T,θ,n button for the variable X.
Press ENTER when you’re done.

Example 1: Graphing a Linear Function
Let’s graph Y = 2X + 5.

Navigate to Y₁.
Type: 2 X,T,θ,n + 5
Do not press ENTER yet. You can enter more functions if you wish.

Example 2: Graphing a Quadratic Function
Let’s add Y = X² - 4 to the same graph.

Press the ▼ down arrow to move to Y₂.
Type: X,T,θ,n x² – 4

Important Notes:

To turn a function off: Use the arrow keys to navigate to the = sign for that function and press ENTER. The = will be highlighted if the function is active and unhighlighted if it is turned off. This is useful for focusing on one graph at a time.
Use parentheses generously to ensure the correct order of operations. For example, to graph Y = 1 / (X + 2), you must type 1 ÷ ( X,T,θ,n + 2 ).

3. Step 2: Setting the Viewing Window

The window defines what you see. The default window is often X: [-10, 10] and Y: [-10, 10] with a scale of 1. Press the WINDOW button to adjust these settings.

The key values to set are:

Xmin: The smallest value on the X-axis (left side).
Xmax: The largest value on the X-axis (right side).
Xscl: The spacing between tick marks on the X-axis (set to 1 for a clean grid).
Ymin: The smallest value on the Y-axis (bottom).
Ymax: The largest value on the Y-axis (top).
Yscl: The spacing between tick marks on the Y-axis.

What if I don’t know what window to use? Use the ZOOM menu.

4. Step 3: Graphing the Functions

Once your functions are entered, press the GRAPH button. The calculator will draw all active functions in the Y= list within your current window.

If you used our examples, you should now see a straight line (Y₁ = 2X + 5) and a parabola (Y₂ = X² - 4) on the same coordinate plane.

5. Step 4: Adjusting the Graph for a Better View

Often, your graph might be off-screen or too zoomed in/out. Here’s how to fix it.

Using the ZOOM Menu

Press the ZOOM button for a list of quick options. The most useful are:

6: ZStandard: Resets the window to the default X: [-10, 10], Y: [-10, 10]. Always try this first.
0: ZoomFit: A fantastic tool. It calculates the Y-min and Y-max needed to show all of your function for the current X-min and X-max. If your graph is cut off vertically, ZoomFit will fix it.
2: Zoom In / 3: Zoom Out: Allows you to draw a box around an area to zoom in or out. Press ENTER to set the box.
5: ZSquare: Adjusts the window so that one unit on the X-axis is the same physical length as one unit on the Y-axis. This makes circles look like circles, not ovals.

Using the WINDOW Manually

After graphing, you can manually adjust the window. If your graph is too far to the right, increase Xmin and Xmax. If it’s too zoomed in, make the difference between min and max larger.

6. Step 5: Analyzing the Graph with the CALC Menu

This is where the TI-84 becomes incredibly powerful. Press 2nd then TRACE (CALC) to access the calculation menu.

Key Options:

1: value: Type in an X-value, and it will calculate the corresponding Y-value for you.
2: zero: Finds the x-intercepts (roots) of a function.
- The calculator will ask for a “Left Bound.” Move the cursor to the left of the zero and press ENTER.
- It will ask for a “Right Bound.” Move the cursor to the right of the zero and press ENTER.
- For “Guess,” press ENTER again.
- It will display the coordinates of the zero (e.g., X=-2, Y=0).
3: minimum / 4: maximum: Finds the local minimum or maximum of a function (the vertex of a parabola). The process is the same as finding a zero: provide left and right bounds.
5: intersect: Finds the point of intersection between two graphs.
- Select this option.
- The cursor will be on the first curve. Press ENTER to select it.
- Move the cursor to the second curve. Press ENTER.
- For “Guess,” press ENTER.
- It will display the (X, Y) coordinates where the two graphs cross.

Example: Use 5: intersect on the two graphs from our example (Y₁ = 2X + 5 and Y₂ = X² - 4). You will find two points of intersection.

7. Graphing Different Types of Functions

A. Graphing Piecewise Functions

You must use inequalities to graph piecewise functions.

Example: Graph:

f(X) = { X+2, for X < 1
{ 4, for X ≥ 1

Go to the Y= editor.
In Y₁, enter: (X+2)/(X<1)
In Y₂, enter: 4/(X≥1)

How it works: The calculator evaluates the inequality. If it’s true, it returns 1; if false, it returns 0. Dividing by 1 leaves the function unchanged. Dividing by 0 creates an undefined value, which the calculator won’t plot. This effectively graphs each piece only where its condition is true.

B. Graphing Trigonometric Functions

Crucial: Make sure your calculator is in Radian mode unless the problem specifies degrees. Press MODE and select Radian.

Example: Graph Y = sin(X).

Go to Y₁ and type SIN X,T,θ,n ).
A good window for trig functions is: Xmin: 0, Xmax: 2π (≈6.28), Xscl: π/2 (≈1.57), Ymin: -2, Ymax: 2.

C. Graphing Statistical Scatter Plots

This is a common application.

Press STAT and 1: Edit… Enter your X data into L1 and your Y data into L2.
Press 2nd then Y= (STAT PLOT). Select 1: Plot1.
Turn it On, select the scatter plot icon (first one), set Xlist: L1, Ylist: L2.
Press ZOOM and 9: ZoomStat. This will automatically set the window to fit all your data points.

8. Advanced Features

Changing Line Styles: In the Y= menu, move the cursor to the left of the function name (where the diagonal line is). Press ENTER to cycle through different line styles (e.g., thick, thin, dotted, shaded above/below). This is helpful for distinguishing between similar graphs.
Shading Between Curves: Enter two functions. Move the cursor to the line style area for the second function. Press ENTER repeatedly until you see a triangle pointing up or down. This will shade the area either above or below that curve, relative to the other function.

9. Troubleshooting Common Graphing Problems

“ERR: INVALID DIM”: This usually means your STAT PLOT is turned on and conflicting with your function graph. Press 2nd Y= (STAT PLOT), select the plot, and turn it Off.
The graph is blank: Check three things: 1) Is the function entered correctly? 2) Is the function turned on in the Y= menu? 3) Is your window large enough? Try ZOOM Standard or ZoomFit.
The graph looks jagged or incorrect: This is often a “resolution” issue. Press WINDOW and change Xres to a lower number (like 2). This will make the calculator plot more points, creating a smoother graph.

10. Practice Problems and Applications

Finding Solutions to Equations: To solve X² = 2X + 3, graph Y₁ = X² and Y₂ = 2X + 3. The x-coordinates of their intersections are the solutions.
Calculus: Use the graph to visualize derivatives (slope) and integrals (area under the curve). The CALC menu can numerically find these values.
Real-World Modeling: Graph equations for physics (projectile motion), economics (supply/demand curves), or biology (population growth).

By mastering these steps, you move from simply drawing lines to using the TI-84 as a dynamic tool for exploration and discovery. The ability to visualize mathematics is a key step toward deeply understanding it.

Frequently Asked Questions (FAQs): Graphing on the TI-84

Q1: I pressed GRAPH, but my screen is blank. What did I do wrong?
A blank screen is one of the most common issues, and it usually has one of a few simple fixes:

The function is turned off: Go to your Y= menu. Make sure the = sign for your function is highlighted. If it’s not, use the arrow keys to select it and press ENTER.
Your window is incorrect: Your graph might be drawn outside the portion of the coordinate plane you’re viewing. Press ZOOM and then 6:ZStandard to reset to the default -10 to 10 window. Then press GRAPH again.
A Stat Plot is on: If you’ve used the calculator for statistics, a scatter plot might be turned on and conflicting with your graph. Press 2nd then Y= (for STAT PLOT). Select each plot (1, 2, 3) and ensure they are set to Off.

Q2: What does “ERR: INVALID DIM” mean and how do I fix it?
This error almost always means there is a problem with your STAT PLOT settings or your WINDOW settings.

First, check STAT PLOTS: Press 2nd > Y= > 4:PlotsOff > ENTER. This will turn all stat plots off. Then try graphing again.
Then, check your WINDOW: Ensure your Xmin is less than your Xmax and your Ymin is less than your Ymax. For example, Xmin=10 and Xmax=-10 will cause this error.

Q3: How do I graph a piecewise function?
You graph piecewise functions by using parentheses and inequalities. The calculator interprets “true” as 1 and “false” as 0.
Example: Graph f(x) = { x+2, for x < 1
{ 4, for x ≥ 1

In Y₁, type: (X+2)/(X<1)
In Y₂, type: 4/(X≥1)
This works because for X<1, the denominator is 1 (true), so it graphs (X+2)/1. For X≥1, the denominator is 0 (false), making the first function undefined (and not graphed) in that region, while the second function takes over.

Q4: My graph looks really choppy and jagged, not smooth. How can I fix this?
This is often due to the calculator’s plotting resolution. To get a smoother graph:

Press the WINDOW button.
You’ll see a setting called Xres. This controls the resolution. The default is 1.
Change Xres to a lower number, like 2 or 3. This tells the calculator to plot more points, creating a smoother curve. Be aware that a lower Xres will make the graph draw slightly slower.

Q5: How do I find the X-value for a specific Y-value?
You have two main options:

Use the TRACE feature: Press TRACE and use the left and right arrow keys to move the cursor along the curve. The X and Y coordinates are displayed at the bottom. This gives you an approximate answer.
Use the CALC Value feature: This is more precise. Press 2nd > TRACE (CALC) > 1:value. Type the Y-value you are interested in and press ENTER. The calculator will show you the corresponding X-value on the graph. Note: If there are multiple X-values for that Y-value, it will show you the one closest to the cursor’s current position.

Q6: What’s the difference between “Zero” and “Intersection” in the CALC menu?

2: Zero finds the point where a single function crosses the X-axis. This is the root or solution of the function when set to zero. The Y-value will always be zero.
5: Intersection finds the point where two functions cross each other. This is the solution to a system of equations (where the two functions are equal). The Y-value will be the output of both functions at that shared X-value.

Q7: How do I graph a vertical line? (Like x = 3)
The TI-84 is designed to graph functions, which, by definition, must pass the vertical line test. A vertical line is not a function. However, you can approximate it with a very steep line.

Try graphing Y₁ = 100000(X - 3). This will create a line so steep it will appear vertical on most screens.
For most practical purposes, it’s better to just use the TRACE feature and remember that for a vertical line at x=3, the X-coordinate will always be 3 for any point on that line.

Q8: I’m graphing trig functions, but they look wrong. What’s happening?
This is almost certainly a mode issue. Check if your calculator is in the correct angle mode.

Press the MODE button.
Look at the third line. If you are working in radians, Radian should be highlighted. If you are working in degrees, Degree should be highlighted.
If you graph sin(X) in radian mode, you’ll get a standard wave that crosses at π, 2π, etc. If you graph it in degree mode, it will be incredibly stretched out, as it would cross at 90, 180, etc. For most high school and college math courses, you will use Radian mode.

Q9: How do I delete a function I no longer want to graph?
Navigate to the Y= menu. Use the arrow keys to go to the function you want to delete. Press the CLEAR button. This will erase the entire equation from that Y= slot.

Q10: Can I save a picture of my graph?
If you have a TI-84 Plus CE or similar color model, you can use the built-in Screen Capture tool.

Press 2nd > PRGM (DRAW) > 2:ScreenCapture.
Select 1:StorePic to save the current graph screen.
Later, you can recall it by selecting 2:RecallPic.
This is useful for comparing graphs or saving a visual for your work. Standard TI-84 Plus models do not have this image-saving functionality.