What are the asymptotes of #y=2/(x+1)-4# and how do you graph the function?

1 Answer
Feb 22, 2017

This type of question is asking you think about how numbers behave when grouped together in an equation.

Explanation:

#color(blue)("Point 1")#

It is not allowed (undefined) when a denominator takes on the value of 0. So as #x=-1# turns the denominator into 0 then #x=-1# is an 'excluded value

#color(blue)("Point 2")#

It is always worth investigation when the denominators approach 0 as this is usually an asymptote.

Suppose #x# is tending to -1 but from the negative side. Thus #|-x|>1#. Then #2/(x+1)# is a very large negative value the -4 becomes insignificant. Thus limit as #x# tends to negative side of -1 then #x+1# is negatively minute so #y=-oo#

In the same way as x tends to the positive side of -1 then #x+1# is positively minute so #y=+oo#

#color(blue)("Point 3")#

As x tends to positive #oo# then #2/(x+1)# tends to 0 so #y=2/(x-1)-4# tends to - 4 on the positive side

You have the same as x tends to negative #oo# in that y tends to - 4 but on the negative side.
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#color(blue)("In conclusion")#

You have a horizontal asymptote at #y=-4#

You have a vertical asymptote at #x=-1#

Tony B