How would I go about sketching a graph for x = y^3 - 16y ?

Answer 1

x = y^3 - 16y

factorizing,

x = y(y^2 - 16)

x = y(y - 4)(y + 4)

The solutions:

y = 0, y = 4 and y = -4

These are the points when x = 0

Now, just test the inbetween values of:

when y = 2

x = (2)^3 - 16(2) = 8 - 32 = -24


when y = -2

x = (-2)^3 - 16(-2) = -8 + 32 = 24

Now, you can sketch the graph which will look like the letter S passing through the origin.

Answer 2

The answer to this depends on what level of mathematics you are studying.

The simple lower level solution is to pick a number of values for y, and calculate what value of x you get. Plot each of these points on graph paper, then sketch a curve that joins them up smoothly. The disadvantage of this method is that it may overlook some significant portion of the graph because it might be so small that it lies between two points.

The advanced level method is to do some simple calculus on the function and find out where all the significant points are. Find out the answers to the following questions:

1. For what values of y is x = 0?
2. For what values of x is y = 0?
3. What way does the derivative behave?
4. What does the function do as y tends to infinity?
5. What does the function do as y tends to minus infinity?
6. For what values is the derivative zero. These are the maxima and minima, and turning points.

With all this information you should be able to sketch the graph of any function.

Answer 3

draw your axes and start at say y= -3. do every integer from -3 to say +3. make a table with you y values on one side and the x values on the other. put a number in for y and you'll get an outcome number which will be your x, of course. To help you graph any function that is x=, just turn your paper counterclockwise 90 degrees and graph like normal (as if it were y= instead). Hope that all made sense and good luck to ya.

Answer 4

Its easy u can even do it on excel or u can do it on paper , make two rows and 10 columns ,on the first column and first row wrire x and on the 2nd row first column right y , u have to insert different values of y to get differnt values of x .First go for those points that are specific for a cubic equation i.e. it must pass through origion so when u put y=0 u get x=0 second thing differentiate the eqation and get its limiting values those would show the asymtotes of the equation at which it becomes infinity the asymtotes would be parallel to x axis and in between u get the points , try doing it on excel u would easily understand , a helpful hint is to go to this website and download the software http://www.mathgv.com/

Answer 5

Use a handful of sample points -- when y is 1, x is -15, etc. -- and sketch from there.

Answer 6

differentiate it by y it will be:
x'=3y^2-16
x'=0-->y1=+4/sqrt(3) and y2=-4/sqrt(3)
y1 is your local minimum,y2 local max
at y=0 the curvature alters
now start from (+inf,+inf) go to(x(y1),y1) go back to zero, go to
(x(y2),y2), got to (-inf,-inf)