Question

f(x)= x^3-1/ x^2+x+1. Find the domain, zeros, holes, and asymptotes

Answer 1

do you know how to factor the difference of two cubes?

Answer 2

(x-1)(x^2+x+1)

Answer 3

yes

Answer 4

now cancel and you are done

Answer 5

I don't know how to factor the denominator

Answer 6

take a look at your numerator in factored form

Answer 7

ohhhhh wowww

Answer 8

\[\frac{(x-1)(x^2+x+1)}{x^2+x+1}\] no need to factor
in fact you cannot factor further, \(x^2+x+1\) has no zeros

Answer 9

so what is the domain?

Answer 10

since the denominator has no zeros, the domain is all real numbers

Answer 11

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?

Answer 12

yeah b/c it can only be factored with imaginary numbers

Answer 13

right

Answer 14

what are the asymptotes....I know its oblique

Answer 15

hold the phone

Answer 16

the whole thing is just the line \(f(x)=x-1\)

Answer 17

it is a line
it does not have asymptotes

Answer 18

I thought you looked for the horizontal asymptote based on the exponents

Answer 19

normally you would

Answer 20

but in this case the entire denominator cancels

Answer 21

\[\frac{(x-1)(x^2+x+1)}{x^2+x+1}=x-1\]

Answer 22

oh alright thank you!