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Chapter 7: Problem 29

Graph each equation in Exercises 21-32. Select integers for \(x\) from \(-3\) to 3 , inclusive. \(y=x^{3}\)

Short Answer

Expert verified
The graph of the equation \(y=x^{3}\) is a cubic curve crossing the origin (0,0) that swoops downward to the left and upward to the right. It passes through the points (-3,-27), (-2,-8), (-1,-1), (0,0), (1,1), (2,8), (3,27).

Step by step solution

01

Define the range of \(x\)

The problem states that \(x\) should range from -3 to 3, inclusive. Therefore, defined values for \(x\) are: -3, -2, -1, 0, 1, 2, and 3.
02

Calculate the corresponding \(y\) values

Substitute each value of \(x\) into the equation \(y=x^{3}\) to find \(y\). This will give you a series of ordered pairs which consist of the values of \(x\) and their corresponding \(y\) values.\ \n For \(x=-3\), \(y=(-3)^{3}=-27\),\ For \(x=-2\), \(y=(-2)^{3}=-8\),\ For \(x=-1\), \(y=(-1)^{3}=-1\), \ For \(x=0\), \(y=0^{3}=0\),\ For \(x=1\), \(y=1^{3}=1\), \ For \(x=2\), \(y=2^{3}=8\),\ For \(x=3\), \(y=3^{3}=27\).
03

Plot the points on the graph

Now that you have a set of ordered pairs, you can plot these points onto a graph. The x-coordinate corresponds to the horizontal positioning, while the y-coordinate corresponds to the vertical positioning on the graph.
04

Draw the graph

After plotting all points, connect them to get the cubic curve, completing the graph of the equation \(y=x^{3}\). Note that an appropriate scale should be chosen so that all points will be properly displayed on the graph.

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