Dear friends, Please read our latest blog post for an important announcement about the website. ❤, The Socratic Team

How do you find the range of a function algebraically #y=(x+5)/(x-2)#?

2 Answers
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources
preview
?

Answer

Write a one sentence answer...

Answer:

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

120
Apr 13, 2015

To best way to find the range of a function is to find the domain of the inverse function. To find the inverse function of a function you have to substitue #x# with #y#, and vice versa, and then find #y#.

So:

#y=(x+5)/(x-2)rArrx=(y+5)/(y-2)rArrx(y-2)=y+5rArr#

#xy-2x=y+5rArrxy-y=2x+5rArry(x-1)=2x+5rArr#

#y=(2x+5)/(x-1)# and its domain is #(-oo,1)uu(1,+oo)# that is, also, the range of your function.

Was this helpful? Let the contributor know!
1500
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources
preview
?

Answer

Write a one sentence answer...

Answer:

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

25
mason m Share
Jan 2, 2016

Answer:

#(-oo,1)uu(1,+oo)#

Explanation:

There will be a break in the range at any horizontal asymptote.

Since the degree of the numerator and denominator are equal, take and divide the coefficients of the terms with the largest degree.

Both of these terms are #x#, and #1/1=1#. Thus, there is a horizontal asymptote at #y=1#.

The range is #(-oo,1)uu(1,+oo)#.

graph{((x+5)/(x-2)-y)(y-1)=0 [-28.45, 29.27, -12.3, 16.57]}

Was this helpful? Let the contributor know!
1500