Question

graph the function y=-1/2x^3 Plot five points one point with x=0, two points with negative x-values, and two points with positive x-values.

Answer 1

For
`\(y = -(1)/(2)x^3\)`, plotted points include (0, 0), (-1, -0.5), (-2, -4), (1, -0.5), and (2, -4), representing key values for x, demonstrating the function's behavior on a graph.

Given the function
`\(y = -(1)/(2)x^3\),` let's find the corresponding
`\(y\)-` values for various
`\(x\)-` values:

When
`\(x = 0\)` :

`\[y = -(1)/(2) * 0^3 = 0\]`

So, the point is (0, 0).

For negative
`\(x\)-` values:

When
`\(x = -1\)` :

`\[y = -(1)/(2) * (-1)^3 = -(1)/(2)\]`

The point is (-1, -0.5).

When
`\(x = -2\)`

`\[y = -(1)/(2) * (-2)^3 = -4\]`

The point is (-2, -4).

For positive
`\(x\)` -values:

When \(x = 1\):

`\[y = -(1)/(2) * 1^3 = -(1)/(2)\]`

The point is (1, -0.5).

When
`\(x = 2\)`:

`\[y = -(1)/(2) * 2^3 = -4\]`

The point is (2, -4).

Plotting these points on a graph gives a visual representation of the function
`\(y = -(1)/(2)x^3\)`.