update readme file

Author: HalemoGPA

readme.md

@@ -37,3 +37,65 @@ This project is a simple function plotter application built using PySide2 for th
 To run the application, execute the following command:
 ```bash
 python src/main.py
+```
+
+## Examples
+
+### Basic Function Input
+- **Function:** `5*x^3 + 2*x`
+- **Range:** `0` to `10`
+- **Expected Output:** Parabolic curve.   <br>   
+![Basic Function](screenshots/ex1.jpg)
+
+
+### Invalid Character in Function
+- **Function:** `5*x^3 + 2*x + !`
+- **Range:** `0` to `10`
+- **Expected Output:** Error message: "Function contains invalid characters."   <br>   
+![Invalid Character](screenshots/ex2.jpg)
+
+
+### Complex Formula Function
+- **Function:** `5*x^3 + 2*x -4/x + 7`
+- **Range:** `-10` to `10`
+- **Expected Output:** Combined plot of Cubic and rational functions.   <br>   
+![Complex Formula](screenshots/ex3.jpg)
+
+
+### Using Sqrt & log10 in Function
+- **Function:** `2*x^4 - log10(x) + sqrt(x)`
+- **Range:** `0` to `50`
+- **Expected Output:** Combined plot of square root, logarithm, and quadratic function.   <br>   
+![Complex Formula](screenshots/ex4.jpg)
+
+
+### Negative Input to sqrt or log10
+- **Function:** `2*x^4 - log10(x) + sqrt(x)`
+- **Range:** `-50` to `500`
+- **Expected Output:** Error message: "Min value must be non-negative for functions with log10 or sqrt."   <br>  
+![Negative Input](screenshots/ex5.jpg)
+
+
+### Wrong Input for Min and Max Values
+- **Function:** `x`
+- **Range:** `a` to `2`
+- **Expected Output:** Error message: "Min and Max values must be numbers."    <br>  
+![Wrong Input](screenshots/ex7.jpg)
+
+
+
+### Using -inf and +inf for min and max values
+- **Function:** `x`
+- **Range:** `-inf` to `inf`
+- **Expected Output:** Straight 45deg line from -inf to +inf    <br>  
+![Wrong Input](screenshots/ex8.jpg)
+
+### Constant Function Formula
+- **Function:** `5`
+- **Range:** `-10` to `10`
+- **Expected Output:** Straight horizontal line from -inf to +inf    <br>  
+![Wrong Input](screenshots/ex9.jpg)
+
+
+## automated tests. run some automated tests using `pytest`
+![img](screenshots\ex10.jpg)