'''
Plotting Functions

In this exercise you will practise how to plot functions with Python. 
Plotting functions is used, for example, to predict data trends or visualise 
mathematical results. The first exercise will be done for you as an example.
'''

'''
Example: A polynomial function

Exercise: Plot the function f(x) = 3x^5 - 2x^2 - 3 in the interval [-1, 1].

Solution steps: 
1. Define the function you want to plot.
2. Define the values for the `x`-axis.
3. Calculate the `y`-values using your function.
4. Use matplotlib to visualise the results. Don't forget to give the plot a 
title and annotate the axes.
'''

import numpy as np
import matplotlib.pyplot as plt

def polynomial(x):    # We first define the function to be plotted
    return 3*x**5 - 2*x**2 - 3

x_axis = np.linspace(-1,1,100) # Define the x-axis within the limits

y_values = polynomial(x_axis) # Calculate the y-values

plt.plot(x_axis,y_values) # Plot the function
plt.title("Plot of a polynomial function") # Give the plot a title
plt.xlabel("x-values") # x-axis label
plt.ylabel("y-values") # y-axis label


'''
Exercise A: A polynomial function - Do it yourself

Plot the polynomial function a * x^3 + b for 3 values of `a` or `b`, 
between -1 and 1. How does your chosen parameter influence the function? 
'''

# Your code here

'''
Exercise B: Two functions in the same plot

Take the functions f(x) = 3 - 2x and f(x) = 2 + 3x, plot them in the same plot 
and find the intersection point by looking at the graph. Determine for 
yourself the appropriate `x` and `y` bounds such that the point of intersection 
is easy to read.

Remember to add a legend, a title and axis labels. You can add a legend by 
including `label = "3 - 2x"` in the parameters for `plt.plot()` 
(so `plt.plot(*plotting parameters*,label = "3 - 2x")`) and then adding a line
`plt.legend()`.
'''

# Your code here