College Algebra 'Asymptotes'

Vertical Asymptote:

• cannot divide by 0
• found by setting the denominator equal to zero and solving for x
• remember to factor completely first

Horizontal Asymptote:

• found by looking at the leading terms of the numerator and the denominator
• the horizontal asymptote= ax^# (term of numerator)/ bx^# (term of denominator)
• if the numerator has a lower degree that the denominator, then there is horizontal asymptote; y=0
• if the numerator and denominator have the same degree, then simplify the leading coefficients; y=a/b

Oblique Asymptote

• found by looking at the leading terms of the numerator and the denominator
• oblique asymptote= ax^# (term of numerator)/ bx^# (term of denominator)
• if the numerator exponent is EXACTLY one more than the denominator, then there will be an oblique asymptote. to find it, divide and disregard the remainder, set the quotient equal to y