Chapter 0.2, Problem 20E

(a)

To determine

To find: The domain and range of the given function.

Answer to Problem 20E

The domain is equal to $\left(-2,2\right)$ and the range is equal to $\left[-\frac{1}{2},\infty \right)$ .

Explanation of Solution

Given information:

The function is $y=\frac{1}{\sqrt{4-x^2}}$ .

Calculation:

The given function is $y=\frac{1}{\sqrt{4-x^2}}$ .

Using the graphing tool, to draw the graph of the function.

  

From the graph of the function, the domain of the function $\frac{1}{\sqrt{4-x^2}}$ is below:

  $x\in \left(-2,2\right)$

From the graph of the function, the range of the function $\frac{1}{\sqrt{4-x^2}}$ is below:

  $R=\left[-\frac{1}{2},\infty \right)$

Hence, the domain is $\left(-2,2\right)$ and the range is $\left[-\frac{1}{2},\infty \right)$ .

(b)

To determine

To sketch: The graph of the function $y=\frac{1}{\sqrt{4-x^2}}$ .

Explanation of Solution

Given information:

The function is $y=\frac{1}{\sqrt{4-x^2}}$ .

Calculation:

The given function is $y=\frac{1}{\sqrt{4-x^2}}$ .

The given function with vertex is $\left(0,\frac{1}{2}\right)$ and vertical asymptotes are $x=-2$ and $x=2$ .

Now, sketch the graph of the function below: