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:
-
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
-
Window Settings
The 10 Essential Functions
1. Linear Function (y = 2x + 1
)
Steps to Plot:
- Press
Y=
- Enter "2X + 1" for Y₁
- 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:
- Press
Y=
- Enter "X²" (use
x²
button or ^2
)
- 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:
- Press
Y=
- Enter "X^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:
- Press
Y=
- Press
MATH
- Select "abs("
- Enter "abs(X)"
- 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:
- Press
Y=
- Enter "2^X"
- 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:
- Press
Y=
- Press
LN
- Enter "ln(X)"
- 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:
- Press
Y=
- Press
SIN
- Enter "sin(X)"
- 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:
- Press
Y=
- Press
COS
- Enter "cos(X)"
- 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:
- Press
Y=
- Press
TAN
- Enter "tan(X)"
- 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:
- Press
Y=
- Press
MATH
- Select "√("
- Enter "√(X)"
- 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
-
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
-
Zooming and Tracing
- Use
ZOOM
menu for preset views
TRACE
to examine specific points
WINDOW
to customize viewing area
-
Finding Key Points
- Use
2nd
+ TRACE
(CALC) menu
- Options include:
- Zero (roots)
- Maximum/minimum
- Intersections
- Derivatives
Troubleshooting Common Issues
-
Graph Not Visible
- Check
WINDOW
settings
- Verify function entry
- Ensure appropriate scaling
- Try
ZOOM
Standard
-
Error Messages
- Check parentheses matching
- Verify domain restrictions
- Confirm angle mode settings
-
Unexpected Results
- Review function syntax
- Check mode settings
- Consider domain restrictions
Practice Exercises
To master these plotting techniques:
- Plot combinations of functions
- Explore transformations
- Analyze intersections
- Study domain and range
- 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.