Chapter 1, Problem 28RE

(a)

To determine

To find: The domain of the function $y=-2+\sqrt{1-x}$ .

Answer to Problem 28RE

The domain of the function $y=-2+\sqrt{1-x}$ is the interval $\left(-\infty ,1\right]$ .

Explanation of Solution

Given information:

The given function is $y=-2+\sqrt{1-x}$ .

Calculation:

Domain is the set of all input values such that the function is define.

The function $y=-2+\sqrt{1-x}$ is defined for all the values of $x$ such that $1-x\ge 0$ .

  $x\le 1$

Therefore, the domain of the function $y=-2+\sqrt{1-x}$ is the interval $\left(-\infty ,1\right]$ .

(b)

To determine

To find: The range of the function $y=-2+\sqrt{1-x}$ .

Answer to Problem 28RE

The range of the function $y=-2+\sqrt{1-x}$ is the interval $\left[-2,\infty \right)$ .

Explanation of Solution

Given information:

The given function is $y=-2+\sqrt{1-x}$ .

Calculation:

Obtain the range of the function.

Since $\sqrt{1-x}\ge 0$ , subtract $2$ from both sides of the inequality gives $-2+\sqrt{1-x}\ge -2$ .

Therefore,the range of the function $y=-2+\sqrt{1-x}$ is the interval $\left[-2,\infty \right)$ .

(c)

To determine

To graph: The function $y=-2+\sqrt{1-x}$ .

Explanation of Solution

Given information:

The given functionis $y=-2+\sqrt{1-x}$ .

Graph:

To graph a function $y=-2+\sqrt{1-x}$ , follow the steps using graphing calculator.

First press “ON” button on graphical calculator, press $\boxed{\text{Y}=}$ key and enter right hand side of the equation $y=-2+\sqrt{1-x}$ after the symbol ${\text{Y}}_1$ . Enter the keystrokes $\boxed{(-)}\boxed{2}\boxed{+}\boxed{2\text{nd}}\boxed{x^2}\boxed{1}\boxed{-}\boxed{\text{X}}\boxed{)}$ .

The display will show the equation,

  ${\text{Y}}_{\text{1}}=-2+\sqrt{1-\text{X}}$

Now, press the $\boxed{\text{GRAPH}}$ key and $\boxed{\text{TRACE}}$ key to produce the graph of both the equations as shown below.

  

Figure (1)

Interpretation: From the above graph it can be observed that the graph is half-parabola opening to the left.