Chapter 6.3, Problem 24PPS

To determine

The domain and range of the function $f\left(x\right)=\sqrt{x-4}-10$ . And sketch the graph of the function.

Answer to Problem 24PPS

The domain of the function is $\left\{x|x\ge 4\right\}$ and range of the function is $\left\{y|y\ge -10\right\}$ .

Explanation of Solution

Given information: The given function is,

  $f\left(x\right)=\sqrt{x-4}-10\mathrm{....}\left(1\right)$

Calculation: The domain of the function is defined for which,

  $\begin{array}{c}x-4\ge 0\\ x\ge 4\end{array}$

Hence the domain of the function is $\left\{x|x\ge 4\right\}$ .

And range of the function can be evaluated by substituting the lower limit of domain in the function for which the function is defined. Therefore from (1),

  $\begin{array}{c}f\left(4\right)=\sqrt{\left(4\right)-4}-\mathrm{10......}\left(\text{For }x=4\right)\\ =-10\end{array}$

Hence the range of the function is $\left\{y|y\ge -10\right\}$

Graph: The graph for the function is shown as,