lisa123
  • lisa123
f(x)= x^3-1/ x^2+x+1. Find the domain, zeros, holes, and asymptotes
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
do you know how to factor the difference of two cubes?
lisa123
  • lisa123
(x-1)(x^2+x+1)
anonymous
  • anonymous
yes

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
now cancel and you are done
lisa123
  • lisa123
I don't know how to factor the denominator
anonymous
  • anonymous
take a look at your numerator in factored form
lisa123
  • lisa123
ohhhhh wowww
anonymous
  • anonymous
\[\frac{(x-1)(x^2+x+1)}{x^2+x+1}\] no need to factor in fact you cannot factor further, \(x^2+x+1\) has no zeros
lisa123
  • lisa123
so what is the domain?
anonymous
  • anonymous
since the denominator has no zeros, the domain is all real numbers
anonymous
  • anonymous
normally you would say "all real numbers except for the zeros in the denominator" but this denominator doesn't have any is it clear why?
lisa123
  • lisa123
yeah b/c it can only be factored with imaginary numbers
anonymous
  • anonymous
right
lisa123
  • lisa123
what are the asymptotes....I know its oblique
anonymous
  • anonymous
hold the phone
anonymous
  • anonymous
the whole thing is just the line \(f(x)=x-1\)
anonymous
  • anonymous
it is a line it does not have asymptotes
lisa123
  • lisa123
I thought you looked for the horizontal asymptote based on the exponents
anonymous
  • anonymous
normally you would
anonymous
  • anonymous
but in this case the entire denominator cancels
anonymous
  • anonymous
\[\frac{(x-1)(x^2+x+1)}{x^2+x+1}=x-1\]
lisa123
  • lisa123
oh alright thank you!

Looking for something else?

Not the answer you are looking for? Search for more explanations.