Quiz 1B Math

Horizontal Case 1

the leading terms have the same degree (n=d)

result: horizontal asymptote that is the ratio of the leading term coefficients y= a/b

Horizontal Case 2

the denominator dominates the numerator (n<d)

result: horizontal asymptote of y=0

Horizontal Case 3

the numerator dominates the denominator (n>d)

result: NO HORIZONTAL ASYMPTOTE

y=x

y = x²

y=x³

y= 1/x

for rational funcs the denominator

can’t equal 0

Degrees divided

subtraction

Special cases

the degree of the numerator is exactly 1 more than the degree of the denominator

result: oblique(slant) asymptote

Slant asymptote is long division (ignore remainder)

vertical asymptote

set denominator equal to zero

BUT if the factor cancels out its a hole