Simplify by combining like terms. 8x + 9 - 4x + 12
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Function A: 
. Vertical asymptotes are in the form x=, and they are a vertical line that the function approaches but never hits. They can be easily found by looking for values of <em>x</em> that can not be graphed. In this case, <em>x</em> cannot equal 0, as we cannot divide by 0. Therefore <em>x</em>=0 is a vertical asymptote for this function. The horizontal asymptote is in the form <em>y</em>=, and is a horizontal line that the function approaches but never hits. It can be found by finding the limit of the function. In this case, as <em>x</em> increases, 1/<em>x</em> gets closer and closer to 0. As that part of the function gets closer to 0, the overall function gets closer to 0+4 or 4. Thus y=4 would be the horizontal asymptote for function A.
Function B: From the graph we can see that the function approaches the line x=2 but never hits. This is the vertical asymptote. We can also see from the graph that the function approaches the line x=1 but never hits. This is the horizontal asymptote.
Function B: From the graph we can see that the function approaches the line x=2 but never hits. This is the vertical asymptote. We can also see from the graph that the function approaches the line x=1 but never hits. This is the horizontal asymptote.