Question

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

Answer 1

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 rarr -oo) f(x)=0`

and

`lim_ (x rarr 7^-) f(x)=oo`

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 rarr oo) f(x)=0`

`lim_ (x rarr 7^+) f(x)=-oo`

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