You can just change the values for a and b in the plot statement to plot other 
functions.  Use different combinations of the values 1, 2, and  3 for a and b.  
Discuss the  effect the exponent has on the graph. Remember that the exponents for the function g are a/3 and b. Use terms like horizontal and vertical tangents, turning point or extrema, inflection point, and passes through the x axis.  Copy the plot statement and insert text for your discussion.  Replace this text with your own....

surd[n_,x_]:=If[Mod[n,2]==0,x^(1/n),Piecewise[{{x^(1/n),x≥0},{-(-x)^(1/n),x<0}}]]
f[x_,a_,b_]:=surd[3,(x+2)^a] (x-1)^b
Plot[f[x,2,3],{x,-2.5,1.5}]