SOLUTION: I wanted to know how to graph the equation of xy=4. I need to find the center and the equations of the asymptotes. Thank you sooo much for your help!!!!!!!!

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I wanted to know how to graph the equation of xy=4. I need to find the center and the equations of the asymptotes. Thank you sooo much for your help!!!!!!!!      Log On


   

Question 130959: I wanted to know how to graph the equation of xy=4.
I need to find the center and the equations of the asymptotes.
Thank you sooo much for your help!!!!!!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
xy=4 Start with the given equation


y=4%2Fx Divide both sides by x to isolate y




In order to graph f%28x%29=4%2Fx, we need to plot some points. To do that, we need to plug in some x values to get some y values


So let's find the first point:



f%28x%29=4%2Fx Start with the given function


f%28-4%29=4%2F%28-4%29 Plug in x=-4


f%28-4%29=-1 Divide -4 into 4 to get -1


So when x=-4, we have y=-1


So our 1st point is (-4,-1)


-------------- Let's find another point --------------


f%28x%29=4%2Fx Start with the given function


f%28-3%29=4%2F%28-3%29 Plug in x=-3


f%28-3%29=-1.3333 Divide -3 into 4 to get -1.33333333333333


So when x=-3, we have y=-1.33333333333333


So our 2nd point is (-3,-1.33333333333333)


-------------- Let's find another point --------------


f%28x%29=4%2Fx Start with the given function


f%28-2%29=4%2F%28-2%29 Plug in x=-2


f%28-2%29=-2 Divide -2 into 4 to get -2


So when x=-2, we have y=-2


So our 3rd point is (-2,-2)


-------------- Let's find another point --------------


f%28x%29=4%2Fx Start with the given function


f%28-1%29=4%2F%28-1%29 Plug in x=-1


f%28-1%29=-4 Divide -1 into 4 to get -4


So when x=-1, we have y=-4


So our 4th point is (-1,-4)


-------------- Let's find another point --------------


f%28x%29=4%2Fx Start with the given function


f%281%29=4%2F%281%29 Plug in x=1


f%281%29=4 Divide 1 into 4 to get 4


So when x=1, we have y=4


So our 5th point is (1,4)


-------------- Let's find another point --------------


f%28x%29=4%2Fx Start with the given function


f%282%29=4%2F%282%29 Plug in x=2


f%282%29=2 Divide 2 into 4 to get 2


So when x=2, we have y=2


So our 6th point is (2,2)


-------------- Let's find another point --------------


f%28x%29=4%2Fx Start with the given function


f%283%29=4%2F%283%29 Plug in x=3


f%283%29=1.3333 Divide 3 into 4 to get 1.33333333333333


So when x=3, we have y=1.33333333333333


So our 7th point is (3,1.33333333333333)


-------------- Let's find another point --------------


f%28x%29=4%2Fx Start with the given function


f%284%29=4%2F%284%29 Plug in x=4


f%284%29=1 Divide 4 into 4 to get 1


So when x=4, we have y=1


So our 8th point is (4,1)


Now lets make a table of the values we have calculated 



 xy



 -4-1
 

 -3-1.33333333333333
 

 -2-2
 

 -1-4
 

 14
 

 22
 

 31.33333333333333
 

 41
Now plot the points



Now connect the points to graph y=4%2Fx (note: the more points you plot, the easier it is to draw the graph)



From this graph, we can see that the center is (0,0), the vertical asymptote is x=0 and the horizontal asymptote is y=0