Appendix
A-9: Graphing
Example A-9.2
Obtain Figure A-9.2(a), a graph of the piecewise function
fx=2 x+1x<210−3 xx≥2
Since the two rules comprising fx are just linear functions joined at x=2, the domain of the graph has been chosen to satisfy 0≤x≤4.
plot(piecewise(x<2,2*x+1,x>=2,10-3*x), x = 0 .. 4, discont = true, labels = [x, y], symbol=solidcircle, symbolsize=15, scaling=constrained);
Figure A-9.2(a) Graph of a discontinuous piecewise function
Solution
Interactive Solution
Expression palette: Piecewise template Fill in the fields as appropriate.
Context Panel: Plots≻Plot Builder≻2-D plot x: 0 to 4 2-D Options: discont
2 x+1x<210−3 xx≥2
Alternatively, clicking this button will launch the Interactive Plot Builder with the given piecewise function already installed. (The Preview and Options buttons will work, but no graph will be embedded in this worksheet.)
Set 0≤x≤4 See Figure A-9.2(b)
Options: Range from/to≻ Insert y as Label Options: Symbol→solid circle Options: Size from 10 to 15 Options: Constrained Scaling Options: Find Discontinuities See Figure A-9.2(c)
Figure A-9.2(b) First pane of the Plot Builder
Figure A-9.2(c) Options panel for the Plot Builder
Coded Solution
Enter the piecewise function.
Execute the plot command below.
f≔piecewisex<2,2 x+1,x≥2,10−3 x
f≔2x+1x<210−3x2≤x
plotf,x=0..4,discont=true,labels=x,y,symbol=solidcircle,symbolsize=15,scaling=constrained
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