Question

the graph of a polynomial function is given. what is the smallest degree that the polynomial could have?

the smallest degree the polynomial could have is
(simplify your answer.)

Explanation:

Identify the turning points of the graph

Using the Turning Points knowledge point

$$ \text{Number of local extrema (peaks and valleys)} = 3 $$

Determine the minimum degree from turning points

Using the Degree of Polynomial and Turning Points knowledge points

$$
LATEXBLOCK0
$$

Analyze end behavior for consistency

Using the End Behavior of Polynomials knowledge point

$$
LATEXBLOCK1
$$

Answer:

The graph of a polynomial function is given. What is the smallest degree that the polynomial could have?

The smallest degree the polynomial could have is <blank>5</blank>
(Simplify your answer.)