Reciprocal Graph Question?

One method of graphing rational functions that are reciprocals of polynomial functions is to sketch the polynomial function and then plot the reciprocals of the y-coordinates of the key ordered pairs.



Use this technique to sketch y=1/f(x) for the function: f(x) = x^3





i dont understand what to do :s can someone explain this to me please
the domain has a restriction. x cannot equal zero (denominator becomes zero). this means your graph will have an asymptote at x = 0. You will plot several key points, connect these key points and run your graph approaching the asymptote.



When you sketch p(x) =x^3 you get these key points



x p(x)

-2, -8

-1, -1

0 , 0

1, 1

2, 8



Your instructions say to plot the reciprocal of the y-coordinate. The points then become



x, f(x)

-2, -1/8

-1, -1

0, 1/0 not allowed, so here is our asymptote

1, 1,

2, 1/8



Plot these main points connect the points on each half of the graph (asymptote divides graph in half)

run your curve towards the asymptote. The x-axis is a horizontal asymptote, so do not cross it. your curve will approach it from underneath on left.side, and approach it from above on the right side.



y = 1/ f(x) has the x-axis as a horizontal asymptote, because as x increases in value, f(x) increases in value, and 1/ f(x) will decrease in value approaching zero, but never equals zero.
Pick some values of x,

x=-1, then f(x)=-1, so 1/f(x) = -1

x=0, then f(x)=0, so 1/f(x) is undefined

x=1, then f(x)=1, so 1/f(x) = 1

x=2, then f(x)=8, so 1/f(x) = 1/8

etc.
The idea is to first sketch f(x) = x^3 by working out the y value for several x values. Then you work out the reciprocal of each y value and plot that at the same x value. Why you would go to all that bother I do not know. It is just as easy to work out 1/x^3 directly and then plot it.