Functions and Their Graphs

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var('x'); y=4/(x^2+2*x-3)

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yb=10; cols=['steelblue','darkblue','purple']

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ll=[r'$y=%s$'%latex(y.factor()),

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    r'$y\prime=%s$'%latex(diff(y,x).factor()),

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    r'$y\prime\prime=%s$'%latex(diff(y,x,x).factor())]

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p=plot([y.factor(),diff(y,x).factor(),

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        diff(y,x,x).factor()],(-5,3),

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       color=cols,thickness=1.5,legend_label=ll)

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p+=sum([point((x0,y(x=x0)),color=cols[0],size=25) 

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        for x0 in [-4,-1,2]])

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p+=line([[-3,-yb],[-3,yb]],color='crimson',linestyle='-.',

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        thickness=3,legend_label=r'$x=-3$')

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p+=line([[1,-yb],[1,yb]],color='red',linestyle='-.',

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        thickness=3,legend_label=r'$x=1$')

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p+=line([[-5,0],[3,0]],color='magenta',linestyle=':',

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        thickness=3,legend_label=r'$y=0$')

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p.set_legend_options(font_size=14,loc=3)

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p.show(gridlines=True,figsize=(6,6),ymin=-yb,ymax=yb)

Language: Sage Gap GP HTML Macaulay2 Maxima Octave Python R Singular

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