document.write( "Question 1113885: f(x) = x^3 − 2x^2 − 4x + 8 / x − 2
\n" ); document.write( "Find any hole(s) in the graph of f.
\n" ); document.write( "Find the zero(s) of f.
\n" ); document.write( "On what interval(s) is f(x) > 0? On what interval(s) is f(x) < 0? (Using interval notation)
\n" ); document.write( "Find the interval(s) on which f is increasing or decreasing. (Using interval notation) \n" ); document.write( "
Algebra.Com's Answer #728967 by greenestamps(13200)\"\" \"About 
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\n" ); document.write( "\"x%5E3-2x%5E2-4x%2B8+=+x%5E2%28x-2%29-4%28x-2%29+=+%28x%5E2-4%29%28x-2%29\"

\n" ); document.write( "So
\n" ); document.write( "\"%28x%5E3-2x%5E2-4x%2B8%29%2F%28x-2%29+=+x%5E2-4\"
\n" ); document.write( "as long as x-2 is not 0.

\n" ); document.write( "So the given function is the same as the function x^2-4 except at x=2, where the given function is undefined.

\n" ); document.write( "So there is a hole in the graph of the given function at x=2. At x=2, the value of the function x^2-4 is 0, so the hole in the graph of the given function is at (2,0).

\n" ); document.write( "The zeros of the given function are the zeros of x^2-4, which are 2 and -2.

\n" ); document.write( "The graph of x^2-4 is a parabola opening upward; the function value is negative between the two zeros of the function and positive \"outside\" the zeros:
\n" ); document.write( "positive on (-infinity, -2) and (2, infinity);
\n" ); document.write( "negative on (-2,2).

\n" ); document.write( "The vertex of x^2-4 is at (0,-4); the function is decreasing on (-infinity, 0) and increasing on (0, infinity). \n" ); document.write( "
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