Graphing Calculator
Graphing Calculator plots mathematical functions (e.g., x^2, sin(x)) with adjustable x and y axis ranges, displaying step-by-step function evaluations.
Methodology Used in Graphing Calculator
The calculator evaluates the function at discrete points and plots them:
Function Evaluation:
1. Parse user-defined function \\( f(x) \\) (e.g., \\( x^2 \\), \\( \sin(x) \\)).
2. For \\( x \\) from \\( x_{\text{min}} \\) to \\( x_{\text{max}} \\) with step \\( \Delta x = \frac{x_{\text{max}} – x_{\text{min}}}{N} \\):
\\[ y_i = f(x_i), \quad x_i = x_{\text{min}} + i \cdot \Delta x, \quad i = 0, 1, \ldots, N \\]3. Map \\( (x_i, y_i) \\) to canvas coordinates and plot.
Where:
- \\( f(x) \\): User-entered function
- \\( x_{\text{min}}, x_{\text{max}} \\): X-axis range
- \\( y_{\text{min}}, y_{\text{max}} \\): Y-axis range
- \\( N \\): Number of points (e.g., 100)
Example Calculation
Sample Input
Function = x^2, X-Min = -2, X-Max = 2, Y-Min = -1, Y-Max = 5
Step 1: Define step size (\\( N = 100 \\)):
\\[ \Delta x = \frac{2 – (-2)}{100} = 0.04 \\]Step 2: Evaluate at sample points (e.g., \\( x = -2, -1.96, \ldots, 2 \\)):
\\[ y(-2) = (-2)^2 = 4, \quad y(-1.96) = (-1.96)^2 \approx 3.8416, \quad \ldots, \quad y(2) = 2^2 = 4 \\]Step 3: Plot points on canvas, scaled to fit \\( y \in [-1, 5] \\).
Result: Parabolic graph of \\( y = x^2 \\).