![(*1*)Clear[f, g, x] ; f[x_] := 0/;x≤0f[x_] := 1/;x>0 ... [x≤0, 1, 2] ; Plot[{f[x], g[x]}, {x, -1, 1}, PlotStyle {Hue[0], Hue[2/3]}]](../HTMLFiles/ex07_solutions_46.gif)
Solutions
I will define functions f and g differently only in order to tell them apart when plotting them.
In[49]:=
![[Graphics:../HTMLFiles/ex07_solutions_47.gif]](../HTMLFiles/ex07_solutions_47.gif)
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In the next excercise, f could be made continuous in a number of ways. They all would call for the redefinition of f in at least one interval. Figure them out if you wish.
In[54]:=
![(*2*)Clear[f, x] f[x_] := x^2/;x<3f[x_] := x + 5/;3≤x<7f[x_] := 14/;x≥7Plot[f[x], {x, 1, 9}]](../HTMLFiles/ex07_solutions_49.gif)
![[Graphics:../HTMLFiles/ex07_solutions_50.gif]](../HTMLFiles/ex07_solutions_50.gif)
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| Created by Mathematica (April 10, 2007) |  |