Chapter 3, Problem 64SGR

To determine

To find: the domain and range of given function.

Answer to Problem 64SGR

The final range of the function is $\left[1,\infty \right)$ .

Domain of the total function is $\left(-\infty ,\infty \right)$ .

Explanation of Solution

Given information:

Given function,

  $f\left(x\right)=\{\begin{array}{l}-3x-2\text{if}x<-1\\ 2x+3\text{if}x\ge -1\end{array}$

Calculation:

Given the $x$ range for the first equation as $x<-1$ .

For the second equation the $x\ge -1$ so these to inequalities covered the entire number line.

Therefore the domain of the function is $\left(-\infty ,\infty \right)$ .

For the first function $-3x-2$ when $x=-1,y=1$ .

When $x=-\infty ,y=\infty$ .

For the second equation when $x=-1,y=1$ when $x=\infty ,y=\infty$ .

So, here observed that the $y$ value will be never less than 1.

So, the range of the function is $\left[1,\infty \right)$ .