Question

consider the following function.
h(x)=-\frac{3}{2}x^{3}
step 2 of 2: find two points on the graph of this function, other than the origin, that fit within the given (-10,10) by (-10,10) grid. express each coordinate as an integer or simplified fraction, or round to four decimal places as necessary.

Explanation:

Step1: Choose an x - value

Let \(x = 2\).

Step2: Calculate the corresponding y - value

Substitute \(x = 2\) into \(h(x)=-\frac{3}{2}x^{3}\). Then \(h(2)=-\frac{3}{2}\times2^{3}=-\frac{3}{2}\times8=- 12\). But \(-12\) is out of the \(y\) - range \([-10,10]\). Let \(x = 1\), then \(h(1)=-\frac{3}{2}\times1^{3}=-\frac{3}{2}\).

Step3: Choose another x - value

Let \(x=-1\).

Step4: Calculate the corresponding y - value

Substitute \(x = - 1\) into \(h(x)=-\frac{3}{2}x^{3}\). Then \(h(-1)=-\frac{3}{2}\times(-1)^{3}=\frac{3}{2}\).

Answer:

The two points are \((1,-\frac{3}{2})\) and \((-1,\frac{3}{2})\)