document.write( "Question 1105987: What's a possible equation for a graph with a vertical asymptote at x=-4, horizontal asymptote at y=0, removable discontinuity at x=4, y-intercept at (0, 1/4) and no x-intercept? \n" ); document.write( "

Algebra.Com's Answer #720900 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "For a vertical asymptote at x=-4, you need a factor of (x+4) in the denominator, with no like factor in the numerator.

\n" ); document.write( "For the removable discontinuity at x=4, you need factors of (x-4) in both numerator and denominator.

\n" ); document.write( "To have no x-intercept, there can be no other linear factors in the numerator.

\n" ); document.write( "Using those constraints, we know parts of the equation are

\n" ); document.write( " $\"%28a%28x-4%29%29%2F%28%28x-4%29%28x%2B4%29%29\"$

\n" ); document.write( "where a is a constant.

\n" ); document.write( "With the equation as it is, it will have a horizontal asymptote of y=0, because the degree of the denominator is greater than the degree of the numerator.

\n" ); document.write( "We want the y-intercept to be (0,1/4); so the equation evaluated at 0 should be 1/4:

\n" ); document.write( " $\"%28a%28x-4%29%29%2F%28%28x-4%29%28x%2B4%29%29+=+%28-4a%29%2F-16+=+a%2F4+-+1%2F4\"$ --> a = 1

\n" ); document.write( "So an equation that has the required features is

\n" ); document.write( " $\"y=%28%28x-4%29%29%2F%28%28x-4%29%28x%2B4%29%29\"$ \n" ); document.write( "

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