+0  
 
0
338
1
avatar+482 

Let
Find the range of \(f(x) = \frac{3x - 7}{x + 1}.\). Give your answer as an interval \(f\).

I am having trouble with this problem. Can someone please help me. Thanks so much. Please explain how you got the answer because I want to know how to solve the problem.

ant101  Apr 2, 2017
Sort: 

1+0 Answers

 #1
avatar+86649 
+1

f(x)  = [ 3x - 7 ] / [ x + 1 ]

 

For rational functions like this that have the same power poynomials in the numerator and denominator.......we can find the horizontal asymptote by dividing the term with the greatest power in the numerator by the term with the greatest power in the denominator.....so

 

3x / [ (1)x ]  =  3

 

So.....we will have a horizontal asymptote at  y = 3

 

And as x approaches -1 from the left, y →  infinity

 

And as x approaches -1 from the right, y → -infinity

 

So....the range is  (-infinity, 3) U (3, + infinity )

 

Here's a graph showing this : https://www.desmos.com/calculator/dq3shmjv9x

 

 

cool cool cool

CPhill  Apr 2, 2017

10 Online Users

avatar

New Privacy Policy (May 2018)

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see cookie policy and privacy policy.