One of the pitfalls of functions in Algebra II is the point of discontinuity. Points of discontinuity, also called removable discontinuities, are moments within a function that are undefined and appear as a break or hole in a graph. A point of discontinuity is created when a function is presented as a fraction and an inputted variable creates a denominator equal to zero. Evaluating a function for points of discontinuity aids in solving and graphing the function.

Obtain the equation of a function. For this example, the expression is f(x) = ( x^2 + x - 2 ) / x-2.

Rewrite the denominator expression as an equation set to zero. For this example, the denominator expression x - 2 becomes the equation x - 2 = 0.

Solve the denominator's equation. For this example, x - 2 = 0 becomes x = 2. The function has a point of discontinuity when x equals 2.

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Chance E. Gartneer began writing professionally in 2008 working in conjunction with FEMA. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. When not working on his children's book masterpiece, he writes educational pieces focusing on early mathematics and ESL topics.