Questions: What is the least possible degree of the polynomial graphed above?

Solution Steps

A turning point is where the graph changes direction from increasing to decreasing or vice versa. Count the number of turning points in the graph.

The maximum number of turning points of a polynomial function is \( n-1 \), where \( n \) is the degree of the polynomial. Therefore, if there are \( k \) turning points, the degree of the polynomial is at least \( k+1 \).

From the graph, count the number of turning points. There are 4 turning points.

Using the relationship \( n-1 = \text{number of turning points} \), we get \( n-1 = 4 \). Therefore, \( n = 5 \).

Final Answer