Chapter 4.1, Problem 61AYU

To determine

To identify: Whether the graph is a polynomial function. If the graph is a polynomial function, then list the real zeros and state the least degree of the polynomial.

Answer to Problem 61AYU

The given graph is a polynomial since the graph is smooth and continuous and has no sharp corners or cusps or holes or gaps and can be drawn without lifting the pencil from paper.

$\text{The real zeros of the polynomial function }f=x\text{-intercept of the graph},f\left(x\right)=0\text{ using the zero product property }=-1,1,2$.

$\text{Least degree of the polynomial function}n=2+1=3$.

Explanation of Solution

Given:

The given graph is a polynomial since the graph is smooth and continuous and has no sharp corners or cusps or holes or gaps and can be drawn without lifting the pencil from paper.

The real zeros of the polynomial function $f=x\text{-intercept}$ of the graph, $f\left(x\right)=0$ using the zero product property = $-1$, 1, 2.

The least degree of the $\text{polynomial function }n=\text{ graph having }\left(n-1\right)\text{ turning points}$.

Number of turning points = 2.

Least degree of the polynomial function $n=2+1=3$.