Question 1006241
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.

For example:
if 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 and you see that the function has a point of discontinuity when {{{x =2}}}


{{{ graph( 600, 600, -20, 20, -20, 20, ( x^2 + x - 2 ) / (x-2)) }}}


as you can see, there is a break or hole in a graph when {{{x=2}}} (I will draw a line to show you that line does not have any common points with a graph of given function



{{{drawing( 600, 600, -20, 20, -20, 20, 
line(2,20,2,-20),
 graph( 600, 600, -20, 20, -20, 20, ( x^2 + x - 2 ) / (x-2))) }}}