Chapter 4, Problem 1RE

To determine

The range of a polynomial function of odd degree having set of real numbers as its domain.

Answer to Problem 1RE

The range of polynomial function of odd degree having set of real numbers as its domain, is  $\underset{\_}{(-\infty ,\infty )}$.

Explanation of Solution

Given:

The polynomial function of odd degree has the set of real of real numbers as its domain.

Definition used:

Polynomial function:

A polynomial function of degree $n$ in the variable  $x$ is a function of form.

$P(x)=a_n{x}^n+a_{n-1}{x}^{n-1}+\mathrm{......}+a_{1}x+a_0,$

Where each $a_i$ is a real number, $a_n\ne 0$, and $n$ is a whole number.

Calculation:

All the polynomial have same domain which consist of all real numbers.

The odd degree polynomial gives value that may include positive number or negative numbers or 0.

Therefore, the range for the odd degree function in interval notation is $(-\infty ,\infty )$.

Thus, the polynomial function of odd degree having set of real numbers as its domain, is $\underset{\_}{(-\infty ,\infty )}$.