Chapter 12, Problem 4CCSR

To determine

To find: the greatest value in the range of the given function $\text{f}\left(\text{x}\right){\text{=x}}^2-3$ having domain $\{-3,0,1,2\}$ .

Answer to Problem 4CCSR

The option $\text{I}$ is correct option.

Explanation of Solution

Given:

  $\text{f}\left(\text{x}\right){\text{=x}}^2-3$ .

Domain= $\{-3,0,1,2\}$ .

Concept used:

the range of the function is so calculated by putting the domain or independent value in side the function and the highest value of the range is called the greatest value of range.

Mathematically,

  $\text{y=f}\left(\text{x}\right)$ .

Here $\text{y=range}$ and $\text{x=domain}$ .

Calculation:

The domain of function is $\text{x}$ and range of function is $\text{f}\left(\text{x}\right)$ .

Given function is $\text{f}\left(\text{x}\right){\text{=x}}^2-3$ and the domains are $\{-3,0,1,2\}$ .

The range of the function will be:

  $\begin{array}{l}\text{f}\left(-3\right)={\left(-3\right)}^2-3=9-3=6.\\ \text{f}\left(0\right)={\left(0\right)}^2-3=-3.\\ \text{f}\left(1\right)={\left(1\right)}^2-3=-2.\\ \text{f}\left(2\right)={\left(2\right)}^2-3=4-3=1.\end{array}$

The greatest range value here is at $\text{x}=-3$ and the greatest value is $\text{6}$ .

Hence, option $\text{I}$ is correct option.