How to Plot 10 Common Functions Using the TI-84 Plus CE Online Calculator

Introduction

The TI-84 Plus CE graphing calculator is a powerful tool for visualizing mathematical functions. This comprehensive guide will walk you through the process of plotting 10 common functions, providing you with the knowledge and skills needed to explore mathematical concepts visually. Whether you're studying algebra, trigonometry, or calculus, mastering these plotting techniques will enhance your understanding of functions and their behaviors.

PS: 10 Common Function Graph Preview Comparison

Basic Calculator Setup

Before we begin plotting functions, it's essential to configure your calculator properly:

1. Screen Settings

   • Press the MODE key
   • Set angle measurements (Degree or Radian)
   • Ensure "Function" plotting is selected
   • Press 2nd + ZOOM (FORMAT) to adjust graph appearance

2. Window Settings

   • Press WINDOW
   • Standard window settings:

     Xmin = -10       Ymin = -10
     Xmax = 10        Ymax = 10
     Xscl = 1         Yscl = 1
     

The 10 Essential Functions

1. Linear Function (y = 2x + 1)

Steps to Plot:

1. Press Y=
2. Enter "2X + 1" for Y₁
3. Press GRAPH

Key Features:

• Constant slope (rate of change)
• Y-intercept at (0, 1)
• Linear pattern
• Domain: all real numbers
• Range: all real numbers

Common Applications:

• Linear relationships in physics
• Cost calculations
• Distance-time relationships

2. Quadratic Function (y = x²)

Steps to Plot:

1. Press Y=
2. Enter "X²" (use x² button or ^2)
3. Press GRAPH

Key Features:

• Parabolic shape
• Vertex at origin (0,0)
• Opens upward
• Domain: all real numbers
• Range: y ≥ 0

Practical Uses:

• Projectile motion
• Optimization problems
• Area calculations

3. Cubic Function (y = x³)

Steps to Plot:

1. Press Y=
2. Enter "X^3"
3. Press GRAPH

Key Features:

• S-shaped curve
• Passes through origin
• Odd symmetry
• Domain: all real numbers
• Range: all real numbers

Applications:

• Volume calculations
• Growth models
• Material stress analysis

4. Absolute Value Function (y = |x|)

Steps to Plot:

1. Press Y=
2. Press MATH
3. Select "abs("
4. Enter "abs(X)"
5. Press GRAPH

Key Features:

• V-shaped graph
• Vertex at origin
• Domain: all real numbers
• Range: y ≥ 0

Real-world Uses:

• Distance calculations
• Error margins
• Financial modeling

5. Exponential Function (y = 2ˣ)

Steps to Plot:

1. Press Y=
2. Enter "2^X"
3. Press GRAPH

Key Features:

• Rapid growth
• Y-intercept at (0,1)
• Domain: all real numbers
• Range: y > 0

Applications:

• Population growth
• Compound interest
• Radioactive decay

6. Natural Logarithm (y = ln(x))

Steps to Plot:

1. Press Y=
2. Press LN
3. Enter "ln(X)"
4. Press GRAPH

Key Features:

• Inverse of exponential function
• Domain: x > 0
• Range: all real numbers
• X-intercept at (1,0)

Practical Uses:

• pH calculations
• Sound intensity
• Information theory

7. Sine Function (y = sin(x))

Steps to Plot:

1. Press Y=
2. Press SIN
3. Enter "sin(X)"
4. Press GRAPH

Key Features:

• Periodic function
• Amplitude = 1
• Period = 2π
• Domain: all real numbers
• Range: [-1, 1]

Applications:

• Sound waves
• Alternating current
• Seasonal patterns

8. Cosine Function (y = cos(x))

Steps to Plot:

1. Press Y=
2. Press COS
3. Enter "cos(X)"
4. Press GRAPH

Key Features:

• Similar to sine, but shifted
• Amplitude = 1
• Period = 2π
• Domain: all real numbers
• Range: [-1, 1]

Real-world Uses:

• Signal processing
• Circular motion
• Navigation

9. Tangent Function (y = tan(x))

Steps to Plot:

1. Press Y=
2. Press TAN
3. Enter "tan(X)"
4. Press GRAPH

Key Features:

• Periodic with vertical asymptotes
• Period = π
• Domain: x ≠ π/2 + πn
• Undefined at asymptotes

Applications:

• Engineering
• Architecture
• Optics

10. Square Root Function (y = √(x))

Steps to Plot:

1. Press Y=
2. Press MATH
3. Select "√("
4. Enter "√(X)"
5. Press GRAPH

Key Features:

• Starts at origin
• Always increasing
• Domain: x ≥ 0
• Range: y ≥ 0

Practical Uses:

• Area calculations
• Statistical analysis
• Physical sciences

Advanced Plotting Tips

1. Multiple Functions

   • Plot multiple functions simultaneously by entering them in different Y= slots
   • Use different colors to distinguish between functions
   • Enable/disable functions using the cursor and ENTER

2. Zooming and Tracing

   • Use ZOOM menu for preset views
   • TRACE to examine specific points
   • WINDOW to customize viewing area

3. Finding Key Points

   • Use 2nd + TRACE (CALC) menu
   • Options include:
     • Zero (roots)
     • Maximum/minimum
     • Intersections
     • Derivatives

Troubleshooting Common Issues

1. Graph Not Visible

   • Check WINDOW settings
   • Verify function entry
   • Ensure appropriate scaling
   • Try ZOOM Standard

2. Error Messages

   • Check parentheses matching
   • Verify domain restrictions
   • Confirm angle mode settings

3. Unexpected Results

   • Review function syntax
   • Check mode settings
   • Consider domain restrictions

Practice Exercises

To master these plotting techniques:

1. Plot combinations of functions
2. Explore transformations
3. Analyze intersections
4. Study domain and range
5. Investigate symmetry

Conclusion

Mastering these 10 common functions on your TI-84 Plus CE calculator opens up a world of mathematical visualization and understanding. Practice regularly with different window settings and combinations of functions to build your graphing expertise. Remember that visualization is a powerful tool for understanding mathematical concepts and their real-world applications.

This guide serves as a foundation for your journey into mathematical visualization. As you become more comfortable with these basic functions, you can explore more complex functions and their applications in various fields of study.