SOLUTION: determine whether the graph of f(x)= x^3-x^2-12x/x-4 has infinite discontinuity, jump discontinuity, point discontinuity, or is continuous

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Question 385615: determine whether the graph of f(x)= x^3-x^2-12x/x-4
has infinite discontinuity, jump discontinuity, point discontinuity, or is continuous

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
determine whether the graph of f(x)= x^3-x^2-12x/x-4
----------------------
has infinite discontinuity, jump discontinuity,
point discontinuity, or is continuous.
----------------------
There is a discontinuity at x = 4
Not sure how you categorize it.
Cheers,
Stan H.

Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

This is undefined when x=4 because the denominator would then be 0.

Factor x out of the numerator:



Factor what is in the parentheses:



This is undefined when x = 4

Now as long as x is not 4, we may cancel the 's, so

the function can be written as

, 

The graph of the function is below and the graph does not contain the
point (4,28).  So there is a point discontinuity at x=4.  Sometimes
this is called a "removable" discontinuity.



Edwin

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