Matplotlib: Plot a Function y=f[x]
In our previous tutorial, we learned how to plot a straight line, or linear equations of type $y=mx+c$.
Here, we will be learning how to plot a defined function $y=f[x]$ in Python, over a specified interval.
We start off by plotting the simplest quadratic equation $y=x^{2}$.
Quadratic Equation
Quadratic equations are second order polynomial equations of type $ax^{2} + bx + c = 0$, where $x$ is a variable and $a \ne 0$. Plotting a quadratic function is almost the same as plotting the straight line in the previous tutorial.
Below is the Matplotlib code to plot the function $y=x^{2}$. It
is a simple straight-forward code; the bulk of it in the middle is for setting the axes. As the exponent of $x$ is $2$, there will only be positive values of $y$, so we can position ax.spines['bottom'] at the bottom.
import matplotlib.pyplot as plt
import numpy as np
# 100 linearly spaced numbers
x = np.linspace[-5,5,100]
# the function, which is y = x^2 here
y = x**2
# setting the axes at the centre
fig = plt.figure[]
ax = fig.add_subplot[1, 1, 1]
ax.spines['left'].set_position['center']
ax.spines['bottom'].set_position['zero']
ax.spines['right'].set_color['none']
ax.spines['top'].set_color['none']
ax.xaxis.set_ticks_position['bottom']
ax.yaxis.set_ticks_position['left']
# plot the function
plt.plot[x,y, 'r']
# show the plot
plt.show[]
Cubic Equation
Next, we will plot the simplest cubic function $y=x^{3}$.
Since the exponent in $y=x^{3}$ is $3$, the power is bound to have negative values for negative values of $x$. Therefore, for visibility of negative values in the $y$-axis, we need to move the $x$-axis to the centre of the graph. ax.spines['bottom'] is thus positioned to centre.
import matplotlib.pyplot as plt
import numpy as np
# 100 linearly spaced numbers
x = np.linspace[-5,5,100]
# the function, which is y = x^3 here
y = x**3
# setting the axes at the centre
fig = plt.figure[]
ax = fig.add_subplot[1, 1, 1]
ax.spines['left'].set_position['center']
ax.spines['bottom'].set_position['center']
ax.spines['right'].set_color['none']
ax.spines['top'].set_color['none']
ax.xaxis.set_ticks_position['bottom']
ax.yaxis.set_ticks_position['left']
# plot the function
plt.plot[x,y, 'g']
# show the plot
plt.show[]
Trigonometric Functions
Here we plot the trigonometric function $y=\text{sin}[x]$ for the values of $x$ between $-\pi$ and $\pi$. The linspace[] method has its interval set from $-\pi$ to $\pi$.
import matplotlib.pyplot as plt
import numpy as np
# 100 linearly spaced numbers
x = np.linspace[-np.pi,np.pi,100]
# the function, which is y = sin[x] here
y = np.sin[x]
# setting the axes at the centre
fig = plt.figure[]
ax = fig.add_subplot[1, 1, 1]
ax.spines['left'].set_position['center']
ax.spines['bottom'].set_position['center']
ax.spines['right'].set_color['none']
ax.spines['top'].set_color['none']
ax.xaxis.set_ticks_position['bottom']
ax.yaxis.set_ticks_position['left']
# plot the function
plt.plot[x,y, 'b']
# show the plot
plt.show[]
Let us plot it together with two more functions, $y=2\text{sin}[x]$ and $y=3\text{sin}[x]$. This time, we label the functions.
import matplotlib.pyplot as plt
import numpy as np
# 100 linearly spaced numbers
x = np.linspace[-np.pi,np.pi,100]
# the function, which is y = sin[x] here
y = np.sin[x]
# setting the axes at the centre
fig = plt.figure[]
ax = fig.add_subplot[1, 1, 1]
ax.spines['left'].set_position['center']
ax.spines['bottom'].set_position['center']
ax.spines['right'].set_color['none']
ax.spines['top'].set_color['none']
ax.xaxis.set_ticks_position['bottom']
ax.yaxis.set_ticks_position['left']
# plot the functions
plt.plot[x,y, 'b', label='y=sin[x]']
plt.plot[x,2*y, 'c', label='y=2sin[x]']
plt.plot[x,3*y, 'r', label='y=3sin[x]']
plt.legend[loc='upper left']
# show the plot
plt.show[]
And here we plot together both $y=\text{sin}[x]$ and $y=\text{cos}[x]$ over the same interval $-\pi$ to $\pi$.
import matplotlib.pyplot as plt
import numpy as np
# 100 linearly spaced numbers
x = np.linspace[-np.pi,np.pi,100]
# the functions, which are y = sin[x] and z = cos[x] here
y = np.sin[x]
z = np.cos[x]
# setting the axes at the centre
fig = plt.figure[]
ax = fig.add_subplot[1, 1, 1]
ax.spines['left'].set_position['center']
ax.spines['bottom'].set_position['center']
ax.spines['right'].set_color['none']
ax.spines['top'].set_color['none']
ax.xaxis.set_ticks_position['bottom']
ax.yaxis.set_ticks_position['left']
# plot the functions
plt.plot[x,y, 'c', label='y=sin[x]']
plt.plot[x,z, 'm', label='y=cos[x]']
plt.legend[loc='upper left']
# show the plot
plt.show[]
Exponential Function
The exponential function $y=e^{x}$ is never going to have any negative values for any value of $x$. So we move the $x$-axis to the bottom again by setting ax.spines['bottom'] to zero. We plot it over the
interval $-2$ to $2$.
import matplotlib.pyplot as plt
import numpy as np
# 100 linearly spaced numbers
x = np.linspace[-2,2,100]
# the function, which is y = e^x here
y = np.exp[x]
# setting the axes at the centre
fig = plt.figure[]
ax = fig.add_subplot[1, 1, 1]
ax.spines['left'].set_position['center']
ax.spines['bottom'].set_position['zero']
ax.spines['right'].set_color['none']
ax.spines['top'].set_color['none']
ax.xaxis.set_ticks_position['bottom']
ax.yaxis.set_ticks_position['left']
# plot the function
plt.plot[x,y, 'y', label='y=e^x']
plt.legend[loc='upper left']
# show the plot
plt.show[]