Both of these, functions and inequalities, are the same because they both deal with polynomial functions and they have similar graphs. They both have constants that are used in their equations, and generally use the same formulas to get the final results. (Factor Theorem, Remainder Theorem). However, these two are different, because a polynomial function can basically be anything and it can have ongoing intervals. There are not many restrictions at all, and the end behaviours always go to either positive or negative infinity. In a polynomial inequality, there are many restrictions. There is always a break in the graph, or the graph is cut off from one side or from both sides at times. There are discontinuties in the graphs of polynomial inequalities and they do not go on, whereas polynomial function graphs are always going on.