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.