This is from the answer key of my alg ii review. can someone explain why each are discontinuities? my teacher never taught us that term so i don’t even know what it means. would be great : )

For

   

x = -2, 2 are discontinuities because they result in a division by zero. division by zero is not allowed/undefined.  (the attachment to my answer  is the graphed function y(

since the denominator comes out to be (x-2)(x+2), that means either x = 2 or x = -2 will make the entire denominator 0 (0 times anything is 0). when the whole denominator becomes zero, you end up dividing by zero, which is undefined. that's why those two values are the discontinuities.

the general idea why it is  called a discontinuity: if you graphed the function out, there would be a visible break in the graph of the function; not everything will be connected and "continuous". 

for 

   

x = 1 is the only discontinuity because it is the only value that results in a division by zero.