Question 8 Given the function $P(x)=x^{3}+3 x^{2}-10 x$. The $y$-intercept is The $x$-intercepts is/are When $x \rightarrow \infty, y \rightarrow ? \vee$ When $x \rightarrow-\infty, y \rightarrow ? \vee$ Question Help: $\square$ Video $1 \square$ Video 2 Submit Question

Step 1 ：The y-intercept of a function is the point where the graph of the function intersects the y-axis. This occurs when x = 0. So, to find the y-intercept, we substitute x = 0 into the function and calculate the corresponding y value. In this case, the y-intercept is \(\boxed{0}\).

Step 2 ：The x-intercepts of a function are the points where the graph of the function intersects the x-axis. This occurs when y = 0. So, to find the x-intercepts, we set the function equal to 0 and solve for x. The x-intercepts of the function are \(\boxed{-5}\), \(\boxed{0}\), and \(\boxed{2}\).

Step 3 ：The limit of a function as x approaches infinity is the value that the function approaches as x gets larger and larger. Similarly, the limit of a function as x approaches negative infinity is the value that the function approaches as x gets smaller and smaller. In this case, the highest degree term is \(x^{3}\), so the limit as x approaches infinity will be determined by the sign of the coefficient of this term, and the limit as x approaches negative infinity will be the opposite of this. Since the coefficient of \(x^{3}\) is positive, the function will approach positive infinity as x approaches positive infinity. Similarly, the function will approach negative infinity as x approaches negative infinity. So, as \(x \rightarrow \infty\), \(y \rightarrow \infty\). As \(x \rightarrow -\infty\), \(y \rightarrow -\infty\).