常見函數

函數的定義：給定一個數集A，對A施加一個對應的法則/映射f，記作：f(A),那麼能夠獲得另一個數集B，也就是能夠認爲B=f(A)；那麼這個關係就叫作函數關係式，簡稱函數。

三個重要因素：定義域A、值域B、對應的映射法則f。

常見函數有：常函數、一次函數、二次函數、冪函數、指數函數、對數函數。

import math
import numpy as np
import matplotlib.pyplot as plt
x = np.arange(0.05,3,0.05)
#常函數
y1 = [5 for i in x]
plt.plot(x,y1,linewidth = 2,label = '常函數:y = 5')
#一次函數
y2 =[2 * i + 1 for i in x ]
plt.plot(x,y2,linewidth = 2,label = '一次函數:y = 2x + 1')
#二次函數
y3 =[1.5 * i * i - 3 * i + 1 for i in x ]
plt.plot(x,y3,linewidth = 2,label = '二次函數:y = 1.5$x^2$ -3x + 1')
#冪函數
y4 =[math.pow(i,2) for i in x ]
plt.plot(x,y4,linewidth = 2,label = '冪函數:y =$x^2$')
#指數函數
y5 =[math.pow(2,i) for i in x ]
plt.plot(x,y5,linewidth = 2,label = '指數函數:y = $2^x$')
#對數函數
y6 =[math.log(i,2) for i in x ]
plt.plot(x,y6,linewidth = 2,label = '對數函數:y = log2(x)')
plt.legend(loc = 'lower right')#顯示圖例大小，其中loc表示位置的；
plt.grid(False)## 顯示背景的網格線，False爲不顯示網絡圖
plt.show()

繪製的圖片中文沒法識別，能夠在配置文件font.sans-serif中添加SimHei、FangSong等中文字體

plt.rcParams['font.sans-serif']=['SimHei']

plt.rcParams['axes.unicode_minus'] = False#解決保存圖像是負號'-'顯示爲方塊的問題

 

 

通常常見函數：

import numpy as np
import matplotlib.pyplot as plt
x1 = np.linspace(-5,5,100)
y3 = [(2 * i + 1 )for i in x1]
plt.plot(x1,y3,label = 'y=2x+10',color = 'b',linewidth = 2)
y4 = [i*i for i in x1]
plt.plot(x1,y4,label = 'y=x^2',color = 'g',linewidth = 2)
y5 = [3 for i in x1]
plt.plot(x1,y5,label = 'y=3',color = 'purple',linewidth = 2)
plt.grid(True)
plt.legend()
plt.show()

 

 

 

import math
import numpy as np
import matplotlib.pyplot as plt
x1 = np.linspace(-5,5,100)
y5 = [3 * math.pow(i,3)for i in x1]
plt.plot(x1,y5,label = 'y=3x^3',color = 'purple',linewidth = 2)
y6 = [10/i for i in x1]
plt.plot(x1,y6,label = 'y=10/x',color = 'k',linewidth = 2)
plt.grid(True)
plt.legend()
plt.show()

 

三角函數：

 

import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(-4*np.pi,4*np.pi,100)
y = [np.sin(i)for i in x]
plt.plot(x,y,label = 'y=sinx',color = 'g',linewidth = 2)
y1 = [np.cos(i)for i in x]
plt.plot(x,y1,label = 'y=cosx',color = 'r',linewidth = 2)
plt.grid(True)
plt.legend(loc='upper right')
plt.xlim(-15,15)
plt.show()

 

對數函數：

import math
import numpy as np
import matplotlib.pyplot as plt
x = np.arange(0.05,3,0.05)
y1 = [math.log(i,0.5)for i in x]
y2 = [math.log(i,math.e)for i in x]#是以e爲底的對數
y3 = [math.log(i,5)for i in x]
y4 = [math.log(i,10)for i in x]
plt.plot(x,y1,label = 'log0.5(x)',color = 'y',linewidth = 2)
plt.plot(x,y2,label = 'loge(x)',color = 'b',linewidth = 2)
plt.plot(x,y3,label = 'log5(x)',color = 'g',linewidth = 2)
plt.plot(x,y4,label = 'log10(x)',color = 'r',linewidth = 2)
plt.plot([1,1],[-3,5],'-',color ='#999999',linewidth = 2)
plt.legend(loc='lower right')
plt.xlim(0,3)
plt.grid(True)
plt.show()