Chapter 6.8, Problem 5SGR

To determine

Whether the statement “A continuous function that can be described by a polynomial equation in one variable is called $\text{polynomial function}$ ”is true or false.

Answer to Problem 5SGR

The statement “A continuous function that can be described by a polynomial equation in one variable is called a $\text{polynomial function}$ ” is true.

Explanation of Solution

Given information:

The statement “A continuous function that can be described by a polynomial equation in one variable is called a $\text{polynomial function}$ ”

Consider the provided statement “A continuous function that can be described by a polynomial equation in one variable is called a $\text{polynomial function}$ ”

The statement is true because A polynomial function is a function which involves only one negative , oe positive or multiplication, subtraction, division integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

A polynomial is generally represented by $P\left(x\right)$ , the highest power of the variable of $P\left(x\right)$ is known as its degree.

For example: Consider a equation as:

  $2x+5$ .

In this polynomial function the exponent is equal to $1$ .

Thus, the statement “A continuous function that can be described by a polynomial equation in one variable is called a $\text{polynomial function}$ ” is true.