Mathematica Tool 2

This Mathematica notebook is designed for  use with Checkpoint 3 in Section 7.1

Part a

(Subscript[f, 1])[x_]:=Sin[x]
Plot[(Subscript[f, 1])[x],{x,-2 π,2 π}]

Part b

(Subscript[f, 2])[x_]:=Sin[(1/x)]
Plot[(Subscript[f, 2])[x],{x,0,1}]

Part c

We calculate this in two parts in order to see the graph of the whole function. Mathematica has a problem with fractional powers of negative numbers. By observing that (x^((-2)/3))= ((((x^2)))^((-1)/3)) we can avoid this problem since (x^2) is always positive.

(Subscript[f, 3])[x_]:=(((((x^2)))^((-1)/3))/3)
Plot[(Subscript[f, 3])[x],{x,-1,1}]

Part d

As in part (c) there are numbers not in the domain of the function. In this case,  x=(Sqrt[2])and x =-(Sqrt[2]). Mathematica can graph the function, but not the vertical lines at x=(Sqrt[2])and x =-(Sqrt[2]) are not real values for the function.

(Subscript[f, 4])[x_]:=((((x^2)+1))/(((x^2)-2)))
Plot[(Subscript[f, 4])[x],{x,-3,3}]