Question

Which description compares the vertical asymptote(s) of Function A and Function B correctly?

Answer 1

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“Function A has a vertical asymptote at x = -4.

Function B has a vertical asymptote at x = 2.”

Answer 2

Function A:  $f(x)=\frac{1}{x}+4$.  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 x that can not be graphed.  In this case, x cannot equal 0, as we cannot divide by 0.  Therefore x=0 is a vertical asymptote for this function.  The horizontal asymptote is in the form y=, 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 x increases, 1/x 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.