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Rational Functions

A rational function can have a variable like "x" in the numerator AND the denominator. When this happens, there are some special rules and properties to consider.

Asymptotes

If the asymptotes of the curve \[y=\frac{6x+10}{x+1}\] are \(x=a\) and \(y=b\), what is the value of \(a+b\)?

If the graph of \[y=\frac{ax-4}{x+b}\] does not intersect either of the lines \(x=4\) or \(y=-4\), what is the value of \(ab\)?

If the asymptotes of the curve \[y-1=\frac{5x-18}{x-5}\] are \(x=a\) and \(y=b\), what is the value of \(a+b\)?

If the asymptotes of the curve \[y=-\frac{1}{x-4}+3\] are \(x=a\) and \(y=b\), what is the value of \(a+b\)?

If the asymptotes of the curve \[y=-\frac{1}{x-4}+11\] are \(x=a\) and \(y=b\), what is the value of \(a+b\)?

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