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

Algebra ->  Graphs -> 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      Log On


   

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

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
%22f%28x%29%22%22%22=%22%22%28x%5E3-x%5E2-12x%29%2F%28x-4%29
This is undefined when x=4 because the denominator would then be 0.

Factor x out of the numerator:

%22f%28x%29%22%22%22=%22%22%28x%28x%5E2-x-12%29%29%2F%28x-4%29

Factor what is in the parentheses:

%22f%28x%29%22%22%22=%22%22%28x%28x-4%29%28x%2B3%29%29%2F%28x-4%29

This is undefined when x = 4

Now as long as x is not 4, we may cancel the %28x-4%29's, so

the function can be written as

%22f%28x%29%22%22%22=%22%22x%28x%2B3%29, x%3C%3E4

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