Thread: Rational Functions - holes

Is it possible to determine the holes of a rational function simply from looking at the graph? If you have ONLY a graph and no equation, can you determine the holes?

Originally Posted by wmountfo

Is it possible to determine the holes of a rational function simply from looking at the graph? If you have ONLY a graph and no equation, can you determine the holes?

Well, it depends. If the graph was drawn out in such a way that the holes were indicated -- usually with an open circle at the point where the hole exists -- then yes. This would mostly apply to a graph that had been drawn by hand since, as far as I know, a standard graphing calculator will not indicate holes in the graph in any visual way. (Of course for a graphing calculator to display a graph, it needs an equation, so it is sort of a moot point.)

Originally Posted by sinewave85

Well, it depends. If the graph was drawn out in such a way that the holes were indicated -- usually with an open circle at the point where the hole exists -- then yes. This would mostly apply to a graph that had been drawn by hand since, as far as I know, a standard graphing calculator will not indicate holes in the graph in any visual way. (Of course for a graphing calculator to display a graph, it needs an equation, so it is sort of a moot point.)

If you move your pointer along a graph used in a graphing calculator, it'll tell you where there are any points of discontinuity though...

Originally Posted by Prove It

If you move your pointer along a graph used in a graphing calculator, it'll tell you where there are any points of discontinuity though...

Yes, it certainly will, and I should have mentioned that. But, you can't see the points just by looking at the graph, at least with my very geriatric TI, and once again you do have an equation to analyze since you have to have an equation to generate a graph...

thanks much

Originally Posted by wmountfo

thanks much

Your welcome!