Question

Which is the graph of the cube root function f(x) = cube root of x

Answer 1

The function is given below as

`f(x)=\sqrt[3]{x}`

Step 1:

We will generate table of values for when x=0

`\begin{gathered} f(x)=\sqrt[3]{x} \\ when\text{ x=1} \\ y=\sqrt[3]{1} \\ y=1 \\ (1,1) \end{gathered}`

When x=-1

`\begin{gathered} f(x)=\sqrt[3]{x} \\ y=\sqrt[3]{-1} \\ y=-1 \\ (-1,-1) \end{gathered}`

when x=0

`\begin{gathered} y=\sqrt[3]{0} \\ y=0 \\ (0,0) \end{gathered}`

When x=8

`\begin{gathered} y=\sqrt[3]{x} \\ y=\sqrt[3]{8} \\ y=2 \\ (8,2) \end{gathered}`

When x=-8

`\begin{gathered} y=\sqrt[3]{-8} \\ y=-2 \\ (-8,-2) \end{gathered}`

The table of values is given below as

Using a graphing calculator, we will have the graph be