Question 385615
{{{"f(x)"}}}{{{""=""}}}{{{(x^3-x^2-12x)/(x-4)}}}
<pre>
This is undefined when x=4 because the denominator would then be 0.

Factor x out of the numerator:

{{{"f(x)"}}}{{{""=""}}}{{{(x(x^2-x-12))/(x-4)}}}

Factor what is in the parentheses:

{{{"f(x)"}}}{{{""=""}}}{{{(x(x-4)(x+3))/(x-4)}}}

This is undefined when x = 4

Now as long as x is not 4, we may cancel the {{{(x-4)}}}'s, so

the function can be written as

{{{"f(x)"}}}{{{""=""}}}{{{x(x+3)}}}, {{{x<>4}}}

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.

{{{drawing(1600/7,800,-4,6,-3,32, graph(1600/7,800,-4,6,-3,32,(x^3-x^2-12x)/(x-4)), circle(4,28,.2)

 )}}}

Edwin</pre>