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instead of Hello folks! In this tutorial, we are going to learn how we can plot mathematical functions using Python. So let’s get started. PrerequisitesFor plotting different mathematical functions using Python, we require the following two Python libraries: 1. NumPyNumPy is a Python library that supports multi-dimensional arrays & matrices and offers a wide range of mathematical functions to operate on the NumPy arrays & matrices. It is one of the most fundamental libraries for scientific computation. We can install NumPy on our local computer using the following command. > python -m pip install numpy 2. MatplotlibMatplotlib is a Python library that is widely used for various types of plotting. Using Matplotlib, We can plot static and interactive visualizations very easily. We can install Matplotlib on our local computer using the following command. > python -m pip install matplotlib First import the import numpy as np import matplotlib.pyplot as plt For all the plottings, we will follow almost the same steps apart from using the specific NumPy mathematical function in the respective plots. 1. Plot (y = x) Identity functionx = np.arange(0, 11, 1) y = x print('Values of x: ', x) print('Values of y: ', y) plt.plot(x, y) plt.title("Identity Function") plt.xlabel("Values of x") plt.ylabel("Values of y") plt.show() Output: Values of x: [ 0 1 2 3 4 5 6 7 8 9 10] Values of y: [ 0 1 2 3 4 5 6 7 8 9 10]Identity Function Plot 2. Plot (y = a.x2 + b.x2 + c) Quadratic functionx = np.arange(-11, 11, 1) a = 2 b = 9 c = 10 y = a*(x**2) + b*x + c print('Values of x: ', x) print('Values of y: ', y) plt.plot(x, y) plt.title("Quadratic Function") plt.xlabel("Values of x") plt.ylabel("Values of y") plt.show() Output: Values of x: [-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10] Values of y: [153 120 91 66 45 28 15 6 1 0 3 10 21 36 55 78 105 136 171 210 253 300]Quadratic Function Plot 3. Plot (y = a.x3 + b.x2 + c.x + d) Cubic functionx = np.arange(-11, 11, 1) a = 2 b = 3 c = 4 d = 9 y = a*(x**3) + b*(x**2) + c*x + d print('Values of x: ', x) print('Values of y: ', y) plt.plot(x, y) plt.title("Cubic Function") plt.xlabel("Values of x") plt.ylabel("Values of y") plt.show() Output: Values of x: [-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10] Values of y: [-2334 -1731 -1242 -855 -558 -339 -186 -87 -30 -3 6 9 18 45 102 201 354 573 870 1257 1746 2349]Cubic Function Plot 4. Plot (y = ln(x) or loge(x)) Natural logarithm functionx = np.arange(1, 11, 0.001) y = np.log(x) print('Values of x: ', x) print('Values of y: ', y) plt.plot(x, y) plt.title("Natural logarithm Function") plt.xlabel("Values of x") plt.ylabel("Values of y") plt.show() Output: Values of x: [ 1. 1.001 1.002 ... 10.997 10.998 10.999] Values of y: [0.00000000e+00 9.99500333e-04 1.99800266e-03 ... 2.39762251e+00 2.39771344e+00 2.39780436e+00]Natural Logarithm Function Plot 5. Plot (y = log10x) Common/Decimal logarithm functionx = np.arange(1, 11, 0.001) y = np.log10(x) print('Values of x: ', x) print('Values of y: ', y) plt.plot(x, y) plt.title("Common logarithm Function") plt.xlabel("Values of x") plt.ylabel("Values of y") plt.show() Output: Values of x: [ 1. 1.001 1.002 ... 10.997 10.998 10.999] Values of y: [0.00000000e+00 4.34077479e-04 8.67721531e-04 ... 1.04127423e+00 1.04131372e+00 1.04135320e+00] Common Logarithm Function Plot 6. Plot (y = ex) Natural Exponential functionx = np.arange(-11, 11, 0.01) y = np.exp(x) print('Values of x: ', x) print('Values of y: ', y) plt.plot(x, y) plt.title("Natural exponential Function") plt.xlabel("Values of x") plt.ylabel("Values of y") plt.show() Output: Values of x: [-11. -10.99 -10.98 ... 10.97 10.98 10.99] Values of y: [1.67017008e-05 1.68695557e-05 1.70390975e-05 ... 5.81045934e+04 5.86885543e+04 5.92783841e+04] 7. Plot (y = ax) General Exponential functionx = np.arange(-11, 11, 0.01) a = 8 y = a**x print('Values of x: ', x) print('Values of y: ', y) plt.plot(x, y) plt.title("General exponential Function") plt.xlabel("Values of x") plt.ylabel("Values of y") plt.show() Output: Values of x: [-11. -10.99 -10.98 ... 10.97 10.98 10.99] Values of y: [1.16415322e-10 1.18861455e-10 1.21358987e-10 ... 8.07043896e+09 8.24001604e+09 8.41315629e+09]General Exponential Function Plot 8. Plot (y = sign(x)) Signum functionx = np.arange(-11, 11, 0.001) y = np.sign(x) print('Values of x: ', x) print('Values of y: ', y) plt.plot(x, y) plt.title("Signum Function") plt.xlabel("Values of x") plt.ylabel("Values of y)") plt.show() Output: Values of x: [-11. -10.999 -10.998 ... 10.997 10.998 10.999] Values of y: [-1. -1. -1. ... 1. 1. 1.]Signum Function Plot 9. Plot (y = a.sin(b.x + c)) Sinusoidal function in Pythonx = np.arange(-11, 11, 0.001) a = 5 b = 3 c = 2 y = a*np.sin(b*x + c) print('Values of x: ', x) print('Values of y: ', y) plt.plot(x, y) plt.title("Sinusoidal Function") plt.xlabel("Values of x") plt.ylabel("Values of y") plt.show() Output: Values of x: [-11. -10.999 -10.998 ... 10.997 10.998 10.999] Values of y: [ 2.02018823 2.03390025 2.04759397 ... -2.10016104 -2.11376421 -2.12734835]Sinusoidal Function Plot 10. Plot (y = sinc(x)) Sinc functionx = np.arange(-11, 11, 0.01) y = np.sinc(x) print('Values of x: ', x) print('Values of y: ', y) plt.plot(x, y) plt.title("Sinc function") plt.xlabel("Values of x") plt.ylabel("Values of y") plt.show() Output: Values of x: [-11. -10.99 -10.98 ... 10.97 10.98 10.99] Values of y: [1.41787526e-16 9.09768439e-04 1.82029537e-03 ... 2.73068428e-03 1.82029537e-03 9.09768439e-04]Sinc Function Plot 11. Plot (y = cosh(x)) Hyperbolic functionx = np.arange(-11, 11, 0.001) y = np.cosh(x) print('Values of x: ', x) print('Values of y: ', y) plt.plot(x, y) plt.title("Hyperbolic Function") plt.xlabel("Values of x") plt.ylabel("Values of y") plt.show() Output: Values of x: [-11. -10.999 -10.998 ... 10.997 10.998 10.999] Values of y: [29937.07086595 29907.14875865 29877.2565585 ... 29847.39423524 29877.25655813 29907.14875828]Hyperbolic Cosine Function Plot Summing-upIn this tutorial, we have learned how to plot different types of mathematical functions using Numpy and Matplotlib libraries. Hope you have understood the plotting process of different mathematical functions and are ready to experiment on your own. Thanks for reading! Stay tuned with us for amazing learning resources on Python programming. To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative. The plot() function is used to draw points (markers) in a diagram. By default, the plot() function draws a line from point to point. The function takes parameters for specifying points in the diagram. |