Could you graph the rational function     `(2x)/ (x^2+2x-15)`

Expert Answers

An illustration of the letter 'A' in a speech bubbles

`y = (2x)/ (x^2+2x-15)`

 

By factoring `x^2+2x-15` you will get `x^2+2x-15 = (x+5)(x-3)`

 

`y = (2x)/((x+5)(x-3))`

Now you can see that at x = -5 and x = 3 the graph goes to `oo` .

Also we can see that at x = 0 then y = 0. This means the graph goes through origin.

 

`y = (2x)/((x+5)(x-3))`

`y = (2x)/(x^2(1+5/x)(1-3/x))`

`y = 2/(x(1+5/x)(1-3/x))`

 

Now it is clear that when `x rarr+-oo` then `y rarr0` .

`lim_(xrarr+-oo)y = 0`

 

The stationary point of the graph is given by the first derivative.

`y = (2x)/ (x^2+2x-15)`

`dy/dx = ((x^2+2x-15)xx2-2x(2x+2))/(x^2+2x-15)^2`

`dy/dx = (2x^2+4x-30-4x^2-4x)/(x^2+2x-15)^2`

`dy/dx = (-2x^2-30)/(x^2+2x-15)^2`

`dy/dx = -(x^2+15)/(x^2+2x-15)^2`

 

Here `(x^2+15)>0` always. So the graph has no real stationary points.

 

Using the data we can plot the graph.

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial