Question

In the following exercise (a) find the domain of the function (b) graph the function (c) use the graph to determine the range of the function:

$f\left(x\right)=\sqrt[3]{x+1}$

Short answer

a) The domain of the function is$\left(-\infty ,\infty \right)$

b) The graph of the function is:

c) The range of the function is$\left(-\infty ,\infty \right)$

Step-by-step solution

Step 1. Given information.

In this case, the following expression is given:

$f\left(x\right)=\sqrt[3]{x+1}$

Step 2. Finding (a) the domain of the function.

Since the index of the radical is 3, the radicand can be any real number. So, the domain of the function will be$\left(-\infty ,\infty \right)$.

Step 3. Constructing (b) the graph of the function.

To construct the graph of the function, we select some sample points from the domain of the function and create a sample table.

Using the table, we construct the graph of the function.

Step 4. Finding (c) the range of the function using the graph.

From the graph, we see that the y values ranges between$-\infty$to$\infty$. So, the range of the function will be$(-\infty ,\infty )$