Functions¶
- Build a linear function $f(x) = -\frac{1}{2}x + 4$ on $x \in [-3, 3]$; create a graph and table.
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import matplotlib.pyplot as plt
import numpy as np
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def f(x): return -0.5*x + 4 #function
x = np.linspace(-3, 3, 100) #domain
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plt.plot(x, f(x)) #plot of function on domain
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import pandas as pd
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f1 = pd.DataFrame({'x': x, 'f(x)': f(x)})
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f1
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- Build a linear function $f(x) = \frac{5}{2}x - 7$ on $x \in [-3, 3]$; create a graph and table.
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def f(x): return (5/2)*x - 7
x = np.linspace(-3, 3, 1000)
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plt.plot(x, f(x))
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f2 = pd.DataFrame({'x': x, 'f(x)': f(x)})
f2.head()
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- Build a quadratic function $f(x) = 3(x - 1)^2 - 4$ on $x \in [-5, 5]$; create a graph and table.
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def f(x): return 3*(x - 1)**2 - 4
x = np.linspace(-5, 5, 100)
plt.plot(x, f(x))
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f3 = pd.DataFrame({'x': x, 'f(x)': f(x)})
f3.head()
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- Build a cosine function $f(x) = 2\cos{x^2}$ on $x \in [-3\pi, 3\pi]$; create a graph and table.
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def f(x): return 2*np.cos(x**2)
x = np.linspace(-3*np.pi, 3*np.pi, 1000)
plt.plot(x, f(x))
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f4 = pd.DataFrame({'x': x, 'f(x)': f(x)})
f4.head()
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- Build an exponential function $f(x) = 3*(100)^x$ on $x \in [-3, 3]$; create a graph and table.
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def f(x): return 3*(100**x)
x = np.linspace(-3, 3, 100)
plt.plot(x, f(x))
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f5 = pd.DataFrame({'x': x, 'f(x)': f(x)})
f5.head()
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