## Function homework question

Limits, differentiation, related rates, integration, trig integrals, etc.
kathrynm77
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Joined: Wed Sep 26, 2012 11:40 pm
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### Function homework question

Let f be the function given by f(x)= 2x/sqrt(x^2 + x + 1)
A) find the domain and justify
B) write an equation for each horizontal asymptote
C) does the graph cross any horizontal asymototes? Show work

So I started this and got
A) domain is all reals because denominator doesn't have restrictions
B) y=2 and y=-2 however I found these graphically and need to know how to do that algebraically
C) yes it crosses y=-2 (I also found this graphically and need it algebraically)

Posts: 136
Joined: Sun Feb 22, 2009 11:12 pm

### Re: Function homework question

Let f be the function given by f(x)= 2x/sqrt(x^2 + x + 1)
A) find the domain and justify
B) write an equation for each horizontal asymptote
C) does the graph cross any horizontal asymototes? Show work

So I started this and got
A) domain is all reals because denominator doesn't have restrictions
B) y=2 and y=-2 however I found these graphically and need to know how to do that algebraically
C) yes it crosses y=-2 (I also found this graphically and need it algebraically)
A) yes, B) yes (but maybe restricted to "as x goes to infinity" for "y=2", etc??), C) yes

B) you can divide by sqrt(x^2). this is |x| so you get

y => -2/sqrt(1+1/x+1/x^2) for x => -infty
y => 2/sqrt(1+1/x+1/x^2) for x => +infty

b/c x/|x| = -1 for x < 0, +1 for x > 0

C) put 2x/sqrt(x^2+x+1) = (asymptote) and solve for x