Question

I need help graphing and I need to know the coordinates. The graph goes up to 12.

Answer 1

We have the next given function:

`f(x)=\sqrt[3]{x}-2`

To find the first point, we need to use:

`\sqrt[3]{x}=0`

Solve the equation for x:

`(\sqrt[3]{x})^3=(0)^3`
`x=0`

So, when x=0, we got the first point (0, -2), because:

`y=\sqrt[3]{x}-2`
`y=0-2`

Then

`y=-2`

Let's find the points on right, let use x=8 and x=27

Replace on the function, when x=8

`y=\sqrt[3]{x}-2`
`y=\sqrt[3]{8}-2`
`y=2-2`
`y=0`

So, it represents the point (8,0)

Now, when x=27

`y=\sqrt[2]{27}-2`
`y=3-2`
`y=1`

This corresponds to the point (27,1)

Now, for points on the left side:

When x=-8

`y=\sqrt[3]{-8}-2`
`y=-2-2=-4`

Which represents the point (-8,-4)

When x=-27

`y=\sqrt[3]{-27}-2`
`y=-3-20-5`

Which represents the point (-27, -5)

Finally, graph these four points on the cartesian plane.