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

\(\text{Range:}\hspace{1mm}(-\infty,+\infty)\)

.
 Sep 21, 2017

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