Question

find seven ordered pairs for the equation y=x^3-8 using the given values of x. then determine its graph

Answer 1

Seven ordered pairs for the equation
`\(y = x^3 - 8\)` can be found by selecting specific values for
`\(x\)` and calculating the corresponding
`\(y\)`values. For example, when
`\(x = -2\), \(y = -16\),` and when
`\(x = 1\), \(y = -7\).`The complete set of ordered pairs provides a representation of the graph of the equation.

Step-by-step explanation:

To find ordered pairs, substitute different values of
`\(x\)` into the equation
`\(y = x^3 - 8\)` and calculate the corresponding
`\(y\)` values. For instance, when
`\(x = -2\),` the calculation is
`\(y = (-2)^3 - 8 = -16\)`. Similarly, for
`\(x = 1\)`, the calculation is
`\(y = 1^3 - 8 = -7\)`. Continue this process with five more values for \(x\) to obtain a total of seven ordered pairs.

The graph of the equation
`\(y = x^3 - 8\)` will represent a cubic function with a vertical shift of 8 units downward compared to the standard cubic function
`\(y = x^3\)`. The ordered pairs generated from the selected
`\(x\)`values will define points on the graph, and plotting these points on a coordinate plane will reveal the curve of the cubic function.

Understanding the behavior of cubic functions is crucial for interpreting the graph. The cubic term
`\(x^3\)` leads to a curve that may exhibit one or more inflection points, and the constant term -8 causes a vertical shift. The seven ordered pairs provide key points on this curve, allowing for a visualization of the graph and facilitating a comprehensive understanding of the behavior of the cubic function.