graph, find x and y intercepts and test for symmetry

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.

## Comments

Ricardo, you may want to revise your solution. Particularly toward the end where you say that the function is not symmetric about the origin. In fact, this function

issymmetric about the origin. You are correct that after replacing x and y with -x and -y respectively, that it results in -x = -y^{3}. But thisisequivalent to the original (multiply both sides by -1), and this is where I think you have made the mistake.