Graphs.md

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Graphs are fundamental when it comes to mathematics.
Equation outputs have patterns that make for interesting graphs when plotted out.
To see these graphs, begin with a simple equation: y = x2. 1. Create a function called "function1" using function declarations.
2. Pass in x and return the square of x.
3. Begin with the def keyword to create a new function with an input of list x from before:

def function1(x):

4. Create a return statement for the result of x squared:

return x * x

This function will square any value you pass it.
The values returned by function1 need to be stored somewhere.
5. Create an empty list called "data" to store these values:

data = [ ]

Find and graph the squares of all the numbers from 1 to 100

Fill data with the squared values returned by function1. Use a for loop to pass in all the numbers from 1 to 100. 1. Create a for loop using the range method:

for i in range(100):

2. Use the list’s append function add it to the list called "data":

output = function1(i)
data.append(output)
import matplotlib.pyplot as plt
import numpy as np

def function1(x):
    return x * x

data = [ ]

for i in range(100):
    output = function1(i)
    data.append(output)

print(data)

3. Pass the list to a Matplotlib plot, like so:

arange(x)

You've graphed all the values from 1 to 100 using a for loop, but you can also do it using a NumPy function for quicker and cleaner code.
Remember the range function Python comes preloaded with?
NumPy has a np.arange(x) function, which produces into a NumPy array from 0 to x.
This function is noninclusive, so it stops right before x.
1. Call data = np.arange(100) to return numbers from 0 to 99.

import matplotlib.pyplot as plt
import numpy as np

def function1(x):
    return x * x

data = np.arange(100)
print(data)

Because NumPy arrays can have one operation performed on them rather than having to make a for loop to iterate through the whole array, you can pass it into a function as if it were a single value. 2. Pass the array data into function1:

output = function1(data)

3. Examine the two ways to graph the squares of all the numbers between 1 to 100.
Both work to produce the same graph, but are achieved through different techniques.

Recap

Matplotlib can also be used to graph equations. There are a lot of customizable options.

• Use a different math formula besides x * x.
• The function you plotted just now is a parabola; try finding the equation of a circle and printing that, as well as a higher-order polynomial. e.g., y = x^3 + x^2 + x.

Full code:

import matplotlib.pyplot as plt
import numpy as np

def function1(x):
    return x * x

data = np.arange(100)
print(data)

output = function1(data)
plt.plot(output)
plt.show()