# How do you graph #f (x) = (24x – 156) /( 36 – x^2)#?

##### 2 Answers

First of all, we have to define the qualitative characteristics of this function. Obviously, it has asymptotes at points where the denominator equals to zero, that is where

Here is one approach to graph this function (and there are others).

Now we have to construct two separate graphs:

and add them up.

Graph of the first function is a hyperbola shifted by 6 units to the left, stretched by a factor of 24 and inverted the sign by reflecting it relative to the X-axis.

graph{-24/(x+6) [-40, 40, -20, 20]}

The graph of the second function can be constructed by inverting the graph of a function

Here is a graph of $g(x)=36-x^2

The resulting graph would look like this:

graph{-24/(x+6)-12/(36-x^2) [-50, 50, -40, 40]}

First of all, we have to define the qualitative characteristics of this function. Obviously, it has asymptotes at points where the denominator equals to zero, that is where

Here is one approach to graph this function (and there are others).

Now we have to construct two separate graphs:

and add them up.

Graph of the first function is a hyperbola shifted by 6 units to the left, stretched by a factor of 24 and inverted the sign by reflecting it relative to the X-axis.

graph{-24/(x+6) [-40, 40, -20, 20]}

The graph of the second function can be constructed by inverting the graph of a function

Here is a graph of

graph{36-x^2 [-80, 80, -40, 40]}

And inverted graph of

graph{-12/(36-x^2) [-80, 80, -40, 40]}

Adding

(1) around point

(2) around point

(3) in between point

(4) to the left of

(5) to the right of

The resulting graph would look like this:

graph{-24/(x+6)-12/(36-x^2) [-50, 50, -40, 40]}