Robert B. answered • 10/18/12

Experienced (15+ years), Patient, Effective.

To Graph:

Create a table of ordered pairs to get a sense of what the graph looks like.

You could begin your table with a few values for x or y. For instance,

y | -2 -1 0 1 2

x | _ _ _ _ _

Now to complete the table, substitute the values for y into the equation, and solve for x. For y = -2, substituting -2 for y in the equation gives

x = (-2)^3, and simplifying this gives x = -8. Now adding this value for x to the table gives

y | -2 -1 0 1 2

x | -8 _ _ _ _

After completing the rest of the table, it should look like this

y | -2 -1 0 1 2

x | -8 -1 0 1 8

and we now can graph the pairs (-8,-2), (-1,-1), (0,0), (1,1), (8,2). Plot these ordered pairs, and you may get an idea of what the graph looks like.

If more pairs are needed it is simply a matter of repeating the process for other values to get enough pairs to recognize the graph.

x and y-intercepts:

Find the x-intercept by substituting 0 for y in the equation and solving for x. The resulting ordered pair(s) will have the form (_,0), and they are your x-intercept(s).

Find the y-intercept by substituting 0 for x in the equation and solving for y. The resulting ordered pair(s) will have the form (0,_), and they are your y-intercept(s).

Test for symmetry:

Test for "horizontal" symmetry by replacing 'x' in every instance with '-x'. If the resulting equation is identical to the original, then the equation has "horizontal" symmetry, also known as "even" symmetry or symmetry over the y-axis.

Test for "vertical" symmetry by replacing 'y' in every instance with '-y'. If the resulting equation is identical to the original, then the equation has "vertical" symmetry, also known as symmetry over the x-axis.

Test for "odd" symmetry by replacing both 'x' and 'y' with '-x' and '-y', respectively. If the resulting equation is identical to the original, then the equation has "odd" symmetry, also known as symmetry over the origin.

I hope this helps. If you need more help, please feel free to ask and I'll be happy to assist you.

Robert B.

I think you mean quadrant I and quadrant III.05/28/21