TI-84 Graphing Functions Tutorial

Master the powerful graphing capabilities of your TI-84 calculator. Learn to plot equations, analyze graphs, use zoom and trace features, and work with advanced graphing modes.

⏱️ 20 min read

👤 Intermediate Level

📈 Graphing Guide

What You'll Learn

1. Setting Up the Graphing Window
2. Plotting Your First Function
3. Trace and Zoom Features
4. Graph Analysis Tools
5. Advanced Graphing Modes
6. Tips and Troubleshooting

📐 Setting Up the Graphing Window

Before plotting any functions, you need to set up an appropriate viewing window. The window determines what portion of the coordinate plane you'll see on the screen.

Understanding the Window Settings

The WINDOW menu controls the boundaries and scale of your graph display. Press WINDOW to access these critical settings.

Setting	Description	Standard Value	When to Change
Xmin	Left boundary of viewing window	-10	When you need to see more negative x-values
Xmax	Right boundary of viewing window	10	When you need to see larger positive x-values
Xscl	Distance between tick marks on x-axis	1	For better readability with different scales
Ymin	Bottom boundary of viewing window	-10	When functions have very negative values
Ymax	Top boundary of viewing window	10	When functions have very large positive values
Yscl	Distance between tick marks on y-axis	1	For better readability with different scales

Standard Window Settings

The TI-84 provides several preset window configurations that work well for different types of problems.

Quick Window Presets:

ZStandard: Press ZOOM → 6 for the standard -10 to 10 window

ZDecimal: Press ZOOM → 4 for nice decimal values when tracing

ZTrig: Press ZOOM → 7 for trigonometric functions

ZSquare: Press ZOOM → 5 for equal x and y scaling

Window Setup Strategy

Start with ZStandard for most functions. If your graph doesn't appear or looks cramped, adjust the window manually. For trigonometric functions, always use ZTrig or set the window manually to show complete periods.

📈 Plotting Your First Function

Now that you understand window settings, let's plot your first function. The Y= editor is where you enter equations to be graphed.

Using the Y= Editor

Press Y= to open the function editor. You can enter up to 10 functions (Y₁ through Y₀) and graph them simultaneously.

Step-by-Step: Graphing y = x²

Open Y= Editor: Press Y= to access the function input screen

Enter Function: In Y₁, type X,T,θ,n then ^ then 2

Set Window: Press ZOOM → 6 for standard window

Graph It: Press GRAPH to see your parabola

📈

y = x² (parabola opening upward)

Multiple Functions

You can graph multiple functions simultaneously by entering them in different Y variables.

Graphing Multiple Functions:

Y₁: Enter X^2 (parabola)

Y₂: Enter 2*X + 1 (linear function)

Y₃: Enter SIN(X) (sine wave)

Graph: Press GRAPH to see all three functions

Function Input Tips

Here are essential techniques for entering functions correctly:

Function Type	Example	Calculator Input	Notes
Linear	y = 2x + 3	2*X + 3	Always use * for multiplication
Quadratic	y = x² - 4x + 1	X^2 - 4*X + 1	Use ^ for exponents
Rational	y = 1/x	1/X	Use parentheses for complex denominators
Exponential	y = 2ˣ	2^X	Or use 2ND + LN for e^X
Trigonometric	y = sin(x)	SIN(X)	Check angle mode (degree/radian)
Logarithmic	y = log(x)	LOG(X)	LOG = base 10, LN = natural log

Common Input Errors

• Forgetting multiplication symbols: Write 2*X, not 2X
• Missing parentheses: Write (X+1)/(X-1), not X+1/X-1
• Wrong variable: Use X,T,θ,n button, not typing the letter X
• Angle mode: Check if trigonometric functions need degrees or radians

🔍 Trace and Zoom Features

Once you've graphed a function, the TRACE and ZOOM features help you explore and analyze the graph in detail. These tools are essential for finding specific values and examining graph behavior.

Using the TRACE Function

The TRACE feature allows you to move along a function and read exact coordinate values.

How to Use TRACE:

Activate TRACE: Press TRACE while viewing a graph

Navigate: Use left and right arrow keys to move along the curve

Switch Functions: Use up and down arrows to move between different graphed functions

Jump to Value: Type a number and press ENTER to jump to that x-value

ZOOM Menu Functions

The ZOOM menu provides powerful tools for adjusting your view of the graph.

ZOOM Option	Key Sequence	Purpose	When to Use
ZBox	ZOOM → 1	Zoom into a rectangular region	Focus on specific area of interest
Zoom In	ZOOM → 2	Magnify around cursor position	Get closer look at specific point
Zoom Out	ZOOM → 3	Reduce magnification	See more of the graph
ZDecimal	ZOOM → 4	Set window for nice decimal values	When tracing and need clean numbers
ZSquare	ZOOM → 5	Make x and y scales equal	For accurate shape representation
ZStandard	ZOOM → 6	Reset to standard -10 to 10 window	Start over with default view
ZTrig	ZOOM → 7	Optimized for trigonometric functions	When graphing sin, cos, tan functions

Advanced ZOOM Techniques

Using ZBox for Precise Viewing:

Select ZBox: Press ZOOM → 1

Set First Corner: Move cursor to one corner of desired area and press ENTER

Set Opposite Corner: Move cursor to opposite corner and press ENTER

Zoom Complete: Calculator automatically zooms to your selected rectangle

TRACE Pro Tips

• Use ZDecimal before tracing for clean decimal coordinates
• Type specific x-values while tracing to jump to exact points
• Press CLEAR to exit trace mode
• Remember that TRACE shows points actually calculated, not every pixel

🔬 Graph Analysis Tools

The TI-84 includes powerful tools for analyzing functions and finding important points like zeros, maximums, minimums, and intersections.

CALC Menu Functions

Press 2ND + TRACE to access the CALC (Calculate) menu with these analysis tools.

Tool	Menu Option	Finds	Common Use
Zero	CALC → 2	x-intercepts (where y = 0)	Solving equations, finding roots
Minimum	CALC → 3	Lowest point in a region	Optimization problems, vertex of parabola
Maximum	CALC → 4	Highest point in a region	Optimization problems, vertex of parabola
Intersect	CALC → 5	Where two functions cross	Solving systems of equations
dy/dx	CALC → 6	Derivative (slope) at a point	Calculus problems, rate of change
∫f(x)dx	CALC → 7	Definite integral	Area under curve, calculus

Finding Zeros (x-intercepts)

Zeros are where the function crosses the x-axis. This is equivalent to solving f(x) = 0.

Step-by-Step: Finding Zeros

Graph Function: Make sure your function is graphed and visible

Access Zero Function: Press 2ND + TRACE → 2

Set Left Bound: Move cursor to left of zero and press ENTER

Set Right Bound: Move cursor to right of zero and press ENTER

Guess: Move cursor near the zero and press ENTER

Finding Maximum and Minimum Points

These tools find the highest and lowest points of a function within a specified interval.

Finding a Minimum (same process for maximum):

Select Minimum: Press 2ND + TRACE → 3

Set Bounds: Set left and right bounds around the minimum point

Get Result: Calculator displays the coordinates of the minimum point

Finding Intersection Points

When you have multiple functions graphed, you can find where they intersect.

Finding Intersections:

Graph Two Functions: Enter functions in Y₁ and Y₂, then graph both

Select Intersect: Press 2ND + TRACE → 5

Choose Functions: Select first curve, then second curve, then guess near intersection

Get Coordinates: Calculator displays exact intersection point

Analysis Tips

• Zoom in for more accurate results
• Set bounds carefully to isolate the point you want
• Some functions may have multiple zeros, maxima, or minima
• If "NO SIGN CHNG" appears, there's no zero between your bounds

⚡ Advanced Graphing Modes

Beyond basic function graphing, the TI-84 supports parametric, polar, and sequence modes for more advanced mathematical applications.

Parametric Mode

Parametric mode allows you to graph curves defined by separate x(t) and y(t) functions.

Setting Up Parametric Mode:

Change Mode: Press MODE, select "Par" (parametric), press ENTER

Enter Equations: Press Y= and enter X₁T and Y₁T functions

Set T Range: Press WINDOW and set Tmin, Tmax, and Tstep values

Graph: Press GRAPH to see the parametric curve

Common Parametric Examples

Curve Type	X₁T	Y₁T	T Range
Circle	cos(T)	sin(T)	0 ≤ T ≤ 2π
Ellipse	3*cos(T)	2*sin(T)	0 ≤ T ≤ 2π
Line	T	2*T + 1	-10 ≤ T ≤ 10
Spiral	T*cos(T)	T*sin(T)	0 ≤ T ≤ 4π

Polar Mode

Polar mode graphs functions of the form r = f(θ), useful for circular and spiral patterns.

Setting Up Polar Mode:

Change Mode: Press MODE, select "Pol" (polar), press ENTER

Enter Equation: Press Y= and enter r₁ as a function of θ

Set θ Range: Press WINDOW and set θmin, θmax, and θstep

Graph: Press GRAPH to see the polar curve

Common Polar Examples

Curve Type	r₁	θ Range	Description
Circle	3	0 ≤ θ ≤ 2π	Circle with radius 3
Rose (4-petal)	sin(2*θ)	0 ≤ θ ≤ 2π	Four-petaled rose
Cardioid	1 + cos(θ)	0 ≤ θ ≤ 2π	Heart-shaped curve
Spiral	θ/2	0 ≤ θ ≤ 6π	Archimedean spiral

Sequence Mode

Sequence mode is used for graphing recursive sequences and series.

Basic Sequence Setup:

Change Mode: Press MODE, select "Seq" (sequence)

Enter Sequence: Press Y= and define u(n), u(nMin), and initial conditions

Set Window: Press WINDOW and set nMin, nMax, and plotting options

Mode Switching Tips

• Always remember to change back to "Func" mode for regular functions
• Each mode has different window settings - check them carefully
• Parametric and polar modes show parameter values when tracing
• Use ZTrig window setting for most trigonometric parametric/polar curves

💡 Tips and Troubleshooting

Even experienced users encounter graphing challenges. Here are solutions to common problems and tips for more effective graphing.

Common Graphing Problems

Problem: Graph doesn't appear

Check Y= equations: Make sure function is entered correctly and highlighted

Adjust window: Try ZStandard or manually set a larger window

Check for restrictions: Functions like 1/x or √x have limited domains

Problem: Graph looks wrong or incomplete

Check parentheses: (X+1)/(X-1) ≠ X+1/X-1

Use ZSquare: For accurate shape representation

Adjust Y-scale: Some functions need much larger or smaller Y-ranges

Problem: TRACE shows wrong values

Use ZDecimal: For clean decimal coordinates when tracing

Check angle mode: Trigonometric functions depend on degree/radian setting

Graphing Best Practices

Situation	Best Practice	Why
Starting any problem	Use ZStandard first	Good default view for most functions
Trigonometric functions	Use ZTrig or set manually	Shows complete periods clearly
Analyzing specific points	Use ZDecimal before tracing	Gives clean coordinate values
Comparing function shapes	Use ZSquare	Equal scaling prevents distortion
Complex expressions	Use plenty of parentheses	Ensures correct order of operations
Multiple functions	Use different line styles	Easier to distinguish curves

Efficiency Tips

Function Memory: Functions stay in Y= editor between sessions
Quick Clearing: Highlight function and press DELETE to remove
Toggle On/Off: Move cursor to = sign and press ENTER to disable function without deleting
Copy Functions: Use 2ND + RCL to copy functions between Y variables
Table View: Press 2ND + GRAPH to see function values in table form
Format Options: Press 2ND + ZOOM for line styles, grid options, and coordinate display

Before Exams or Important Work

• Clear all Y= functions that you don't need
• Reset to Function mode (not parametric, polar, or sequence)
• Check angle mode (degree/radian) for trigonometry problems
• Set window to ZStandard for consistency
• Test basic functions like y=x to ensure calculator is working properly

← Previous: Basic Functions Next: Statistics →

Ready to Master Graphing?

Practice these graphing techniques with our free TI-84 calculator. Try plotting different functions and using the analysis tools to explore mathematical relationships!

📈 Start Graphing Now