We are asked to graph the function $p(x) = -5x^3$. We need to use the graphing tool provided.

1. Problem Description

We are asked to graph the function $p(x) = -5x^3$. We need to use the graphing tool provided.

2. Solution Steps

To graph the function $p(x) = -5x^3$, we can analyze its properties.

First, note that the function is a cubic function.

When $x = 0$, $p(0) = -5(0)^3 = 0$. So, the graph passes through the origin $(0, 0)$.

When $x = 1$, $p(1) = -5(1)^3 = -5$. So, the graph passes through the point $(1, -5)$.

When $x = -1$, $p(-1) = -5(-1)^3 = -5(-1) = 5$. So, the graph passes through the point $(-1, 5)$.

When $x = 2$, $p(2) = -5(2)^3 = -5(8) = -40$. So, the graph passes through the point $(2, -40)$.

When $x = -2$, $p(-2) = -5(-2)^3 = -5(-8) = 40$. So, the graph passes through the point $(-2, 40)$.

The function is an odd function because $p(-x) = -5(-x)^3 = -5(-x^3) = 5x^3 = -p(x)$. So, it has rotational symmetry about the origin. The graph will have a similar shape to the cubic function $y = x^3$, but it will be reflected about the x-axis because of the negative sign, and it will be vertically stretched by a factor of

5.

The points $(0,0)$, $(1,-5)$, and $(-1,5)$ will be sufficient to generate the graph.

3. Final Answer

The graph of $p(x) = -5x^3$ is a cubic function that passes through the origin (0, 0). It also passes through the points (1, -5) and (-1, 5). The graph should be similar to $y = x^3$, but reflected over the x-axis and stretched vertically by a factor of

5. You will need to use the graphing tool to input these points and sketch the graph.