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.
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.