Answer
$(0, 0)$ is on the graph.
$(1, 1)$ is not on the graph.
$(1, -1)$ is on the graph.
Work Step by Step
The points that are on the graph, must satisfy the equation. Therefore we have to see for all three of the points if they satisfy the given equation:
$y=x^3-2\sqrt{x}$
For the first point:
$x=0, y=0$
$y=x^3-2\sqrt{x}\\
0=0^3-2\sqrt0\\
0=0$
The point is on the graph.
For the second point:
$x=1, y=1$
$y=x^3-2\sqrt{x}\\
1=1^2-2\sqrt1\\
1\ne-1$
The point is not on the graph.
For the third point:
$x=1, y=-1$
$y=x^3-2\sqrt{x}\\
-1=1^3-2\sqrt1\\
-1=-1$
The point is on the graph.
