Question

7. For the following function, (a) state the domain, (b) identify all intercepts, and (c) find any vertical or slant
asymptotes.
f(x)=2x^2-5x+5/x-2
8. Divide and simplify the expressions: x^3-y^3/x^2-y^2 divided by x^2+xy+y^2/x-y

Answer 1

#7 f(x) = 2x^2-5x+5/x-2
the domain is all reals except where the denominator is zero
x-intercepts: none, since the discriminant is negative
f(0) = -5/2
vertical asymptote: x = 2
slant asymptote: y=2x-1

#8. assuming the usual carelessness with parentheses, I get

(x^3-y^3)/(x^2-y^2)
------------------------- = (x^3-y^3)/(x^2-y^2) * (x-y)/(x^2+xy+y^2)
(x^2+xy+y^2)/(x-y)

= (x-y)(x^2+xy+y^2) / (x-y)(x+y) * (x-y) / (x^2+xy+y^2)
= (x-y)/(x+y)