Note that they asymptotes are shown as dotted lines

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Unformatted text preview: d so this graph will never cross the y-axis. It does get very close to the y-axis, but it will never cross or touch it and so no y-intercept. Next, recall that we can determine where a graph will have x-intercepts by solving f ( x ) = 0 . For rational functions this may seem like a mess to deal with. However, there is a nice fact about rational functions that we can use here. A rational function will be zero at a particular value of x only if the numerator is zero at that x and the denominator isn’t zero at that x. In other words, to determine if a rational function is ever zero all that we need to do is set the numerator equal to zero and solve. Once we have these solutions we just need to check that none of them make the denominator zero as well. In our case the numerator is one and will never be zero and so this function will have no xintercepts. Again, the graph will get very close to the x-axis but it will never touch or cross it. Finally, we need to address the fact that graph gets very close t...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.

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