Cubic Graph Ac830B

1. The problem asks us to sketch the graph of the function $y = x^3$. 2. The function $y = x^3$ is a cubic function, which means it is a polynomial of degree 3. 3. Important properties of $y = x^3$: - It passes through the origin $(0,0)$. - It is an odd function, symmetric about the origin. - As $x$ increases, $y$ increases rapidly. - As $x$ decreases, $y$ decreases rapidly. 4. The graph is an increasing curve that passes through the origin, with the shape of an S-curve. 5. The function has no intercepts other than the origin. 6. The slope of the curve at any point is given by the derivative $y' = 3x^2$, which is always non-negative, confirming the increasing nature. 7. The graph looks like a smooth curve starting from the bottom left, passing through the origin, and going to the top right. Final answer: The graph of $y = x^3$ is an increasing cubic curve passing through the origin.