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

##### 1 Answer

See explanaition

#### Explanation:

First you should find the vertical asymptotes of the equation. This is done by setting the denominator equal to zero.

so

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

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

and

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:

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