Question 1121879
the equation is y = 11 / (8x^3).


when x = 0, y is undefined.


you would probably want to plot 2 points that are fairly close to 0 on each side to see which way the equation is trending right before it becomes undefined.


you would then probably want to plot 2 points further away on each side to see what else is happening with the curve.


i chose x = 0, plus or minus 1 and plus or minus 2.


when x = 0, y = 11 / 0 which is undefined.


when x = -1, y = 11 / (8 * (-1)^3) = -1.375


when x = -2, y = 11 / (8 * (-2)^3) = -.171875


when x = 1, y = 11 / (8 * 1^3) = 1.375


when x = 2, y = 11 / (8 * 2^3) = .171875


for this type of curve, 5 points is probably not enough, so i would probably want to plot more points to get a better idea of what the curve looks like.


i would pick something even closer to 0 and something even further away than plus or minus 2.


instead, i chose to use graphing software to show me what the curve should look like.


it looks like this:


<img src = "http://theo.x10hosting.com/2018/082701.jpg" alt="###">


if i had chosen values of x closer to 0, i would have seen that the graph rises higher and higher the closer i got to x = 0.


on the left side, it would get more and more negative.
on the right side, it would get more and more positive.


if i had chosen values of x farther from 0, i would have seen that the graph gets closer and closer to y = 0, the further out i went.


on the left side, it would get closer and closer to y = 0 but still remain negative.


on the right side, it would get closer and closer to y = 0 but still remain negative.


to demonstrate, i chose x plus or minus .1 and x = plus or minus 10.


when x = -.1, y = -1375.
when x = .1, y = 1375.


when x = -10, y = -.001375
when x = 10, y = .001375 


to save myself from more manual calculations, i used excel to make a table of selected values to show you what they would tell you about the shape of the curve.


here's the table in excel.


<img src = "http://theo.x10hosting.com/2018/082702.jpg" alt="$$$">


the first two columns show the value of y when x = -20 to 20 in increments of 2.


the second two columns show the value of y when x = -10 to 10 in increments of 1.


the third two columns show the value of y when x = -1 to 1 in increments of .1.


the fourth two columns show the value of y when x = -.1 to .1 in increments of .01.