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

1 Answer
Tony B
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

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