document.write( "Question 1147481: Give an example of a function which is continuous at all points except -1,2 and 10. \n" ); document.write( "

Algebra.Com's Answer #768798 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "A rational function with factors of (x-a) in both numerator and denominator will have a \"hole\" in the graph at x=a -- that is, the graph will be continuous except at x=a.

\n" ); document.write( "The simplest (and not very interesting) function that is continuous everywhere except at x=-1, x=2, and x=10 is the rational function with factors of (x+1), (x-2), and (x-10) in both numerator and denominator:

\n" ); document.write( " $\"f%28x%29+=+%28%28x%2B1%29%28x-2%29%28x-10%29%29%2F%28%28x%2B1%29%28x-2%29%28x-10%29%29\"$

\n" ); document.write( "Clearly that function has the value 1 everywhere that it is defined, which is everywhere except at x=-1, x=2, and x=10.

\n" ); document.write( "To get a more interesting function that satisfies the requirements, add any additional polynomial factors to the numerator. For example, if you add the factor (x^2-5) to the numerator, then the graph will look like the graph of x^2-5 but will have holes at x=-1, x=2, and x=10.

\n" ); document.write( " \n" ); document.write( "

\n" );