Mathematica Tool 3

This notebook supports Activity 5 in Section 1.5. Note Mathematica will yield a complex number whenever taking a fractional power of a negative number, so we have to write the cube root function as piecewise function.

f[x_]:=(x^3)
g[x_]:=(1/(f[x]))
h[x_]:=(Piecewise[{{-((Abs[x])^(1/3)), x<0}, {(x^(1/3)), x≥0}}])

Plot[f[x],{x,-2,2},PlotRange->{{-4,4},{-4,4}}]
Plot[g[x],{x,-4,4},PlotRange->{{-4,4},{-4,4}}]
Plot[h[x],{x,-4,4},PlotRange->{{-4,4},{-2,2}}]

Plot[{f[x],g[x],h[x]},{x,-4,4},PlotRange->{{-4,4},{-4,4}}]