Question

consider the following function. h(x)=-\frac{3}{2}x^{3} step 1 of 2: identify the general shape of the graph of this function.

Explanation:

Step1: Recall polynomial - function shape rules

For a polynomial function \(y = ax^{n}\), the sign of \(a\) and the degree \(n\) determine the shape. Here, \(h(x)=-\frac{3}{2}x^{3}\), the degree \(n = 3\) (odd) and \(a=-\frac{3}{2}<0\).

Step2: Apply odd - degree and negative - leading - coefficient rules

When the degree \(n\) of a polynomial is odd and the leading coefficient \(a<0\), as \(x\to-\infty\), \(y\to\infty\) and as \(x\to\infty\), \(y\to-\infty\). The general shape starts high on the left - hand side and ends low on the right - hand side.

Answer:

The graph starts high on the left and ends low on the right.