A rational equation contains a fraction with a polynomial in both the numerator and denominator — for example; the equation y = (x – 2) / (x^2 – x – 2). When graphing rational equations, two important features are the asymptotes and the holes of the graph. Use algebraic techniques ...
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For graphing functions, we need to take care of domain, range, asymptotes, and holes. Also, we need to know at least two to three points on each part of the curve for graphing the function.
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Otherwise, the easiest way to find discontinuities in your function is to graph it. Take note of any holes, asymptotes, or jumps. These all represent discontinuities, and just one discontinuity is enough to make your function a discontinuous function. See also: Continuity Test. Types of Disconti...
These asymptotes appear at x equals one half pi, at x equals one and a half pi, and so on. This happens because on one side of the asymptote the graph is approaching positive infinity and on the other side it’s approaching negative infinity, and it can’t be both! Another way to ...