Chapter 3.1, Problem 40E

To determine

To calculate: To find the domain and range of the function

Answer to Problem 40E

Domain is $-\infty <x<\infty$

Range is $\left[0,\infty \right)$

Explanation of Solution

Given: Function is $y=\left|x\right|$

Formula Used:

Domain of a function is the set of all possible input values for a function

Range of a function is set of all possible output values for a function

Calculation:

Function is given as follows:

  $y=\left|x\right|$

Domain of Function:

The given function can accept any value of $x$

Thus, domain is $-\infty <x<\infty$

Range of Function:

Range of an absolute function of the form $c\left|ax+b\right|+k$ is $f\left(x\right)\ge k$

Here, $k=0$

  $f\left(x\right)\ge 0$

Thus, range is $\left[0,\infty \right)$

Conclusion:

Hence, Domain is $-\infty <x<\infty$

Range is $\left[0,\infty \right)$