Chapter 0.2, Problem 17E

(a)

To determine

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

Answer to Problem 17E

The domain is equal to $\left(-\infty ,\infty \right)$ and the range is equal to $\left[0,\infty \right)$ .

Explanation of Solution

Given information:

The function is $y=x^{\frac{2}{3}}$ .

Calculation:

The given function is $y=x^{\frac{2}{3}}$ .

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

  

From the graph of the function, the domain of the function $x^{\frac{2}{3}}$ is below:

  $x\in \left(-\infty ,\infty \right)$

From the graph of the function, the range of the function $x^{\frac{2}{3}}$ is below:

  $R=\left[0,\infty \right)$

Hence, the domain is $\left(-\infty ,\infty \right)$ and the range is $\left[0,\infty \right)$ .

(b)

To determine

To sketch: The graph of the function $y=x^{\frac{2}{3}}$ .

Explanation of Solution

Given information:

The function is $y=x^{\frac{2}{3}}$ .

Calculation:

The given function is $y=x^{\frac{2}{3}}$ .

The given function with vertex is $\left(0,0\right)$ .

Now, sketch the graph of the function below: