1. The problem is to graph the function $y=2x^{3}$. 2. The function is a cubic polynomial where the coefficient 2 scales the cubic term $x^{3}$. 3. Important properties: - The graph passes through the origin $(0,0)$ because when $x=0$, $y=0$. - For positive $x$, $y$ increases rapidly since $x^{3}$ grows quickly. - For negative $x$, $y$ decreases rapidly (goes to negative infinity) because $x^{3}$ is negative. 4. The function is odd, symmetric about the origin. 5. To plot, calculate some points: - $x=-2$, $y=2(-2)^{3}=2(-8)=-16$ - $x=-1$, $y=2(-1)^{3}=-2$ - $x=0$, $y=0$ - $x=1$, $y=2(1)^{3}=2$ - $x=2$, $y=2(2)^{3}=16$ 6. The graph is steep and passes through these points, showing the cubic growth scaled by 2. Final answer: The graph of $y=2x^{3}$ is a cubic curve passing through the origin, increasing steeply for positive $x$ and decreasing steeply for negative $x$.