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What are the asymptotes of #y=2/x+3# and how do you graph the function?

Answer 1

#y=3#
#x=0#

I tend to think of this function as a transformation of the function #f(x)=1/x#, which has a horizontal asymptote at #y=0# and a vertical asymptote at #x=0#.

The general form of this equation is #f(x)=a/(x-h)+k#.

In this transformation, #h=0# and #k=3#, so the vertical asymptote is not shifted left or right, and the horizontal asymptote is shifted up three units to #y=3#.

graph{2/x+3 [-9.88, 10.12, -2.8, 7.2]}

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Answer 2

Abigail Allen

The function y=2/x+3 has two asymptotes: a vertical asymptote at x=-3 and a horizontal asymptote at y=0. To graph the function, plot the vertical asymptote at x=-3 as a dashed line. Then, plot points on either side of the vertical asymptote and draw a smooth curve that approaches the asymptote as x approaches positive or negative infinity.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.