For the following graph, determine if the graph represents a polynomial function. If it is a polynomial function, then determine the number of turning points and the least degree possible.

Answer 1

Hi Abdullah,

at least the polynomial function must be 2 it means f(x) = ax^2 + bx +c

Because polynomial such as f(x) = ax^2 + bx + c always f' (x) = 0 has a solution ( there is a number) and behavior of function will change increasing to decreasing or decreasing to increasing.

Note1: function such as f(x) = ax + b represents a line and f'(x) always as a number that it is the slope so the behavior of function doesn't change, always increasing OR decreasing.

Note2: some time the goal of turning point is inflection point

In this case at least polynomial function must be 3 such as f(x) = ax^3 + bx^2 + cx + d

Because inflection point is the answer of f"(x) = 0 Be careful at function f(x) = ax^2 + bx + c

f"(x) is always a number so there is not inflection point.

I hope it is useful,

Minoo