We have the next given function:
[tex]f(x)=\sqrt[3]{x}-2[/tex]
To find the first point, we need to use:
[tex]\sqrt[3]{x}=0[/tex]
Solve the equation for x:
[tex](\sqrt[3]{x})^3=(0)^3[/tex][tex]x=0[/tex]
So, when x=0, we got the first point (0, -2), because:
[tex]y=\sqrt[3]{x}-2[/tex][tex]y=0-2[/tex]
Then
[tex]y=-2[/tex]
Let's find the points on right, let use x=8 and x=27
Replace on the function, when x=8
[tex]y=\sqrt[3]{x}-2[/tex][tex]y=\sqrt[3]{8}-2[/tex][tex]y=2-2[/tex][tex]y=0[/tex]
So, it represents the point (8,0)
Now, when x=27
[tex]y=\sqrt[2]{27}-2[/tex][tex]y=3-2[/tex][tex]y=1[/tex]
This corresponds to the point (27,1)
Now, for points on the left side:
When x=-8
[tex]y=\sqrt[3]{-8}-2[/tex][tex]y=-2-2=-4[/tex]
Which represents the point (-8,-4)
When x=-27
[tex]y=\sqrt[3]{-27}-2[/tex][tex]y=-3-20-5[/tex]
Which represents the point (-27, -5)
Finally, graph these four points on the cartesian plane.
