How many turning points are in the graph of the polynomial function? 2 turning points 3 turning points 4 turning points 5 turning points

four turning points.

Explanation:

The turning points are those points where the graph changes direction, i.e. where the function changes from growing to decreasing or from decreasing to growing.

That is the typical behavior of polinomial and it is related with the degree of the polynomial.

In this case, since you have the graph you can directly telling the turning points. Those are near x = - 2, x = -1, x = 1 and x = 2, i.e. four turning points.

Those turning points correspond to local maxima (if the function changes from growing to decreasing) or local minima (if the function changes from decreasing to growing).

A point of inflection is that point where the function changes sign.
 We then have to look for the slope changes in the given function,
 We have inflection points in:
 4 points of the given graph.
 
 4 turning points