## Precalculus (6th Edition) Blitzer

The possible equation for the given graph is $y=-{{x}^{3}}+2$.
The above given graph looks similar to the graph of the function $y=-{{x}^{3}}$ but the function $y=-{{x}^{3}}$ passes through the origin. So we have a shifted graph. Here, the shown graph passes through the point $\left( 0,2 \right)$, which means that it has a y-intercept of 2. Therefore, the graph is shifted upwards vertically by 2 units. Thus, the graph is shifted upwards by $c$ units. So, the function is of the form $y=-{{x}^{3}}+c$, where the value of $c$ is 2. Therefore, the possible function is $y=-{{x}^{3}}+2$.