Graphing Calculator

Interactive online graphing calculator for plotting and analyzing mathematical functions. Supports linear, quadratic, trigonometric, exponential, logarithmic, and custom functions.

Function Settings

Graph Range

Function Graph

Function curve
Key points

How to Use the Graphing Calculator

  1. Select Function Type: Choose from linear, quadratic, trigonometric, exponential, logarithmic, or custom functions
  2. Enter Parameters: Input the coefficients and parameters for your chosen function type
  3. Adjust Graph Range: Set the X and Y axis ranges to focus on the area of interest
  4. View Live Graph: Watch the function plot update in real-time as you change parameters
  5. Analyze Key Points: Review important points like intercepts, vertices, and critical points
  6. Use Presets: Try the quick preset buttons to explore common mathematical functions
  7. Custom Functions: Enter your own mathematical expressions using standard notation

Examples and Use Cases

Basic Functions

y = 2x + 1
Linear function with slope 2, y-intercept 1
y = x² - 4x + 3
Quadratic parabola with vertex at (2, -1)
y = sin(x)
Basic sine wave with period 2π

Advanced Functions

y = 2 × sin(0.5x + π/4) + 1
Transformed sine: amplitude 2, period 4π, phase shift, vertical shift
y = 2^x
Exponential growth function, base 2
y = log(x + 1)
Logarithmic function shifted left by 1 unit

Understanding the Graph

Function Types

Linear Functions

Straight lines with constant slope. Form: y = mx + b where m is slope and b is y-intercept.

Quadratic Functions

Parabolas opening up or down. Form: y = ax² + bx + c with vertex at x = -b/(2a).

Trigonometric Functions

Periodic functions like sine, cosine, tangent with transformations for amplitude, period, and phase.

Graph Features

Grid and Axes

Coordinate grid with labeled axes helps identify specific points and understand scale.

Key Points

Red dots mark important points like intercepts, vertices, and critical points for analysis.

Range Control

Adjust X and Y ranges to zoom in on specific areas or get a broader view of the function.

Frequently Asked Questions

How do I enter custom functions?

Select "Custom Function" and enter your expression using standard mathematical notation. Use operators like +, -, *, /, ^ for power, and functions like sin(), cos(), log(), sqrt().

What do the red dots on the graph represent?

Red dots mark key points of interest such as y-intercepts for linear functions, vertices for quadratics, and other mathematically significant points that help in function analysis.

Why doesn't my function appear on the graph?

Check that your function parameters create valid outputs and that the graph range includes the area where your function exists. Try adjusting the X and Y range values to see more of the graph.

How do I change the scale of the graph?

Use the X Min/Max and Y Min/Max controls to adjust the viewing window. Smaller ranges zoom in for detail, larger ranges zoom out for a broader view.

Can I plot multiple functions at once?

This calculator shows one function at a time. To compare functions, you can switch between different function types and parameters to analyze their relationships.

What mathematical functions are supported for custom expressions?

Supported functions include basic arithmetic (+, -, *, /, ^), trigonometric (sin, cos, tan), logarithmic (log, ln), square root (sqrt), absolute value (abs), and exponential (exp).

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