What is an example of a function that has a vertical asymptote at #x = -1# and a horizontal asymptote at #y = 2#?

1 Answer
Mar 5, 2018

Answer:

#f(x) (=y) = 2+1/(x+1)#

Explanation:

We know that the relation #haty=1/hatx# has a vertical asymptote at #hatx=0# and a horizontal asymptote at #haty=0#

If we wish to shift all points left one unit (i.e. the vertical asymptote to #x=-1#) then we need to replace #hatx# with #x+1# (so when #x=-1# then #hatx=0#, the vertical asymptote).

Similarly to shift all points up two units (i.e. the horizontal asymptote to #y=2#) we need to replace #haty# with #y-2#

Therefore the required relation would become
#color(white)("XXX")y-2=1/(x+1)#

Converting this into function form (with #y=f(x)#)
we have
#color(white)("XXX")y=2+1/(x+1)#

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