# 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:

$\textcolor{b l u e}{\text{Point 1}}$

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

$\textcolor{b l u e}{\text{Point 2}}$

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 $\frac{2}{x + 1}$ 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 $y = - \infty$

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

$\textcolor{b l u e}{\text{Point 3}}$

As x tends to positive $\infty$ then $\frac{2}{x + 1}$ tends to 0 so $y = \frac{2}{x - 1} - 4$ tends to - 4 on the positive side

You have the same as x tends to negative $\infty$ in that y tends to - 4 but on the negative side.
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$\textcolor{b l u e}{\text{In conclusion}}$

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

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