Chapter 1, Section 2: Preview Activity

a. Determine the values g(−2), g(−1), g(0), g(1), and g(2), if defined. If the function value is not defined, explain what feature of the graph tells you this.

g[t_]:=
If[t==0,1,
If[t≤1,4-t^2,
If[t≠2,3-t]
]
]
p1=Plot[g[t],{t,-2.3,3.5},PlotStyle->{Thickness[0.005]}];
p2=ListPlot[{{0,4},{1,2},{2,1}},PlotStyle->Large,PlotMarkers->{O}];
p3=ListPlot[{{0,1},{1,3}},PlotStyle->Large];
Show[p1,p2,p3,PlotLabel->"Discontinuous Function of Preview 1.2.1",AxesLabel->{"t","y"},AspectRatio->1]
MatrixForm[Table[{x,g[x]},{x,{-2,-1,0,1,2}}]]

b) For each of the values a = −1, a = 0, and a = 2, complete the following sentence : "As x gets closer and closer (but not equal) to a, g (x) gets as close as we want to______."

a=-1: g(-1)=3
a=0: 4
a=2: 1

c. What happens as x gets closer and closer (but not equal) to a=1? Does the function g(x) get as close as we would like to a single value?

No: it’s split. On the left of a=1, it’s approaching 3; on the right, it’s approaching 2.