Chapter 1.2, Problem 8E

(a)

To determine

To find:The domain and range of the function $y=-\sqrt{-x}$ .

Answer to Problem 8E

The domain and range of the function $y=-\sqrt{-x}$ is $\left(-\infty ,0\right]$ and $\left(-\infty ,0\right]$ respectively.

Explanation of Solution

Given information:The given function is $y=-\sqrt{-x}$ .

Calculation:

The function $y=-\sqrt{-x}$ is defined only when $-x\ge 0$ or $x\le 0$ . The domain of the function is the interval $\left(-\infty ,0\right]$ .

The function $\sqrt{-x}$ is always non negativefor $x\le 0$ .

  $\sqrt{-x}\ge 0$

Multiply both sides by $-1$ of the above inequality.

  $-\sqrt{-x}\le 0$

So, the range of the function $y=-\sqrt{-x}$ is the interval $\left(-\infty ,0\right]$ .

Therefore, the domain and range of the function $y=-\sqrt{-x}$ is $\left(-\infty ,0\right]$ and $\left(-\infty ,0\right]$ respectively.

(b)

To determine

To graph:The function $y=-\sqrt{-x}$ .

Explanation of Solution

Given information:The function is $y=-\sqrt{-x}$ .

Graph:

The graph of the function $y=-\sqrt{-x}$ is drawn below:

  

Figure(1)

Interpretation:The graph of the function $y=-\sqrt{-x}$ is an leftwards parabola with vertex at origin defined for only $x\le 0$ .