# How do you graph y=-2/(x-7) using asymptotes, intercepts, end behavior?

Mar 16, 2017

See explanaition

#### Explanation:

First you should find the vertical asymptotes of the equation. This is done by setting the denominator equal to zero.
so $x = 7$ is the vertical asymptote.

Then since the numerator's highest exponent on a variable is lower than the denominator, the horizontal asymptote is $y = 0$

Then you can plug in a point left of the vertical asymptote like 6 for the x value. This will output 2 for the y value. we know it is above the horizontal asymptote so it must be increasing because it cannot cross either the vertical or horizontal asymptote.

You can draw a line that starts horizontally towards the left side and curves upward as it reaches the asymptote (which it never touches).

in other words

${\lim}_{x \rightarrow - \infty} f \left(x\right) = 0$

and

${\lim}_{x \rightarrow {7}^{-}} f \left(x\right) = \infty$

Now you can repeat this same process on the right side of the asymptote.

Plug in a point on the right side of the asymptote for x
you will get a negative value. So you can figure out:

${\lim}_{x \rightarrow \infty} f \left(x\right) = 0$

${\lim}_{x \rightarrow {7}^{+}} f \left(x\right) = - \infty$

graph{-2/(x-7) [-3.88, 16.12, -4, 6]}