1) Explain why the graph represents a function.


2) Where is the function above discontinuous? Describe each kind of discontinuity.


3) Using interval notation, describe the domain and range of the function above.

 Sep 21, 2017

1) The graph above is a function as it passes the vertical line test. 


2) A function is considered to be discontinuous if you cannot outline the entire function with only one stroke of a writing utensil. The discontinuities lie on x=1, x=2, and x=3, assuming the scale of the graph is 1:1. 


At x=1, the type of discontinuity is a jump discontinuity because the linear section of the graph suddenly ends, and a new part of the graph starts again at the same vertical line.


At x=2, that is a removable discontinuity because there is a hole located at (2,0).


At x=3, this is an infinite discontinuity because x=3 is a vertical asymptote. If you identify a vertical asymptote, you have identified an infinite discontinuity.


3) \(\text{Domain:}\hspace{1mm}[0,3)\cup(3,4]\)


 Sep 21, 2017

5 Online Users