Chapter 1.2, Problem 14E

(a)

To determine

To find:The domain and range of the function $y=2\sqrt{3-x}$ .

Answer to Problem 14E

The domain and range of the function $y=2\sqrt{3-x}$ is $\left(-\infty ,3\right]$ and $\left[0,\infty \right)$ respectively.

Explanation of Solution

Given information:The given function is $y=2\sqrt{3-x}$ .

Calculation:

It cab be observed that function $y=2\sqrt{3-x}$ is defined for only $x\le 3$ .So, the domain of the function $y=2\sqrt{3-x}$ is the interval $\left(-\infty ,3\right]$ .

The range is the set of all output values for which function is defined. The function is defined for all positive values. So, the range of the function $y=2\sqrt{3-x}$ is the interval $\left[0,\infty \right)$ .

Therefore, the domain and range of the function $y=2\sqrt{3-x}$ is $\left(-\infty ,3\right]$ and $\left[0,\infty \right)$ respectively.

(b)

To determine

To graph:The function $y=2\sqrt{3-x}$ with the help of graphing calculator.

Explanation of Solution

Given information:The function is $y=2\sqrt{3-x}$ .

Graph:

To graph a function $f\left(x\right)=2\sqrt{3-x}$ , 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 $f\left(x\right)=2\sqrt{3-x}$ after the symbol ${\text{Y}}_1$ . Enter the keystrokes $\boxed{2}\boxed{\times }\boxed{(}\boxed{3}\boxed{-}\boxed{\text{X}}\boxed{)}\boxed{^}\boxed{(}\boxed{1}\boxed{÷}\boxed{2}\boxed{)}$ .

The display will show the equation,

  ${\text{Y}}_{\text{1}}=2*\left(3-\text{X}\right)^\left(1/2\right)$

Now, press the $\boxed{\text{GRAPH}}$ key and $\boxed{\text{TRACE}}$ key to produce the graph of given quadratic equation in standard window as shown below.

  

Figure (1)

Interpretation:The graph of the function $y=2\sqrt{3-x}$ is the rightwards parabola with vertex at origin and defined for only $x\le 3$ .