Chapter 4.9, Problem 23E

(a)

To determine

To find: The degree of the given polynomial function.

Answer to Problem 23E

The required order of the polynomial $f\left(x\right)=-3x+2x^2+1$ is $2$ .

Explanation of Solution

Given information:

The given function is:

  $f\left(x\right)=-3x+2x^2+1$

Consider the given equation:

  $f\left(x\right)=-3x+2x^2+1$

Consider the highest degree from the above polynomial.

The highest degree of the polynomial is $2$ .

Hence, the required order of the polynomial $f\left(x\right)=-3x+2x^2+1$ is $2$ .

(b)

To determine

To find: The degree of the given graph.

Answer to Problem 23E

The required order of the graph is $3$ .

Explanation of Solution

Given information:

The given graph is:

  

Consider the given graph

  

Consider the turns witnessed in the graph.

The graph has $2$ turns, so it has a order of $3$ .

Hence, the required order of the graph is $3$ .

(c)

To determine

To find: The degree of the given values.

Answer to Problem 23E

The the required order of the given values is $1$ .

Explanation of Solution

Given information:

The given graph is:

  

Consider the given values from the table.

  

Apply the finite difference theorem to find the difference.

  

The difference shows that the order is $1$ .

Hence, the required order of the given values is $1$ .

(d)

To determine

To find: The degree of the given values.

Answer to Problem 23E

The required order of the given values is $4$ .

Explanation of Solution

Given information:

The given graph is:

  

Consider the given values from the table.

  

Apply the finite difference theorem to find the difference.

  

The difference shows that the order is $4$ .

Hence, the required order of the given values is $4$ .