Chapter 6.4, Problem 22MCQ

To determine

The graph, domain and range of function $y=\sqrt{x+4}-1$ .

Answer to Problem 22MCQ

The domain of the function is $\left\{x|x\ge -4\right\}$ and range of function is $\left\{y|y\ge -1\right\}$ .

Explanation of Solution

Given information: The given function is,

  $y=\sqrt{x+4}-1$

Calculation: From the function $y=\sqrt{x+4}-1$ the domain is defined for all $\left(x\right)$ belongs to real and $x+4\ge 0$ because the part of function under the root must be greater than or equal to zero. Hence, the domain of function is evaluated as,

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

Hence, the domain $\left(D_f\right)$ of function is $\left\{x|x\ge -4\right\}$ .

Now, the range of the function can be evaluated by plugging the least value of domain $\left(x=-4\right)$ in the given function $y=\sqrt{x+4}-1$ . Therefore the range of the function is evaluated as,

  $\begin{array}{l}y\ge \sqrt{\left(-4\right)+4}-1\\ y\ge -1\end{array}$

Hence, the range $\left(R_f\right)$ of the function is $\left\{y|y\ge -1\right\}$

Graph: The graph for the function is shown as,