9. Rational Functions

Question 1

ƒ is a rational function iff…

Answer 1

ƒ(x) = p(x) / q(x)

where p(x) and q(x) are polynomials and q(x) ≠ 0.

Question 2

ƒ(x) = p(x) / q(x)

If p and q are both 0 for some x…

If q is 0 and p is not 0…

Answer 2

…there is a hole at that x.

…an asymptote results.

Question 3

Horizontal asymptote of ƒ(x) at y = b

when…

Answer 3

lim_x→±∞ ƒ(x) = b

Question 4

Vertical asymptote of ƒ(x) at x=a

when…

Answer 4

lim_x→a^± ƒ(x) = ±∞

Question 5

lim_x→∞ a/x =

Answer 5

0