Free help with homework

Why join Brainly?

  • ask questions about your assignment
  • get answers with explanations
  • find similar questions

Find the equations of the horizontal and vertical asymptotes for the following. Tye none if the function does not have an asymptote.

a. f(x)=2x+3/x+2



This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
As x approaches 0 from  negative side,  f(x) approaches - infinity.  As x approaches 0 from positive side, f(x) approaches positive infinity.

  The slope of tangent of f(x) = f '(x) = 2 - 3/x² 

  Slope approaches minus infinity as x tends to zero.  f(x) is discontinuous at x=0.

So the asymptote is x = 0 as the tangent at x=0 (slope is infinity) is perpendicular to x axis.

  f ' (x) = Slope approaches 2, as x tends to infinity.  So there is an asymptote with slope equal to 2 as x tends to infinity.  we have to find its equation.
   f(x) as x tends to infinity is :  2 x + 2 + 3/infinity  or  2 x + 2
   the second asymptote is  y = 2x + 2

1 5 1
select best answer and click on thank you link
The Brain
  • The Brain
  • Helper
Not sure about the answer?
Learn more with Brainly!
Having trouble with your homework?
Get free help!
  • 80% of questions are answered in under 10 minutes
  • Answers come with explanations, so that you can learn
  • Answer quality is ensured by our experts