graphing

[Integral0]

(1) How do you graph the equation y = 9 divided by x^2 w/o using a calculator and besides plotting points?

(2) If you replace x with y and y with x, can you reflect the equation 9/x^2 ?

thanks

[HallsofIvy]

You can't graph an equation (other than a linear equation) exactly without plotting individual points.

You can get a pretty good approximation by noting that, since x2 is always positive, y= 9/x2 is above the y axis and symmetric about the x axis. Of course, for x close to 0, y will be very large: the y axis is a vertical asymptote. For x very large, y is close to 0: the x axis is a horizontal asymptote.

(2) If you replace x with y and y with x, can you reflect the equation 9/x^2 ?

I presume you mean changing y= 9/x2 into x= 9/y2. Yes, that will "reflect" the graph through the line y= x.