Identifying Asymptotes

1
Identifying Asymptotes

• Vertical Asymptotes
• Set denominator equal to zero and solve x
  value
• Horizontal Asymptotes
• Degree of numerator lt degree of denominator y
  0
• Degree of numerator degree of denominator
• Degree of numerator gt degree of denominator
  none!! Instead, you possibly get a slant
  asymptote
• Slant Asymptotes numerator degree must be
  EXACTLY ONE GREATER than denominator degree
• Long divide the numerator by the denominator,
  disregard the remainder
• y quotient

2
Identify the Asymptotes
Horizontal y 1 Vertical x 3
3
To graph

• Graph the y-intercept Find F(0)
• Graph the x-intercept Set numerator 0
• Graph the vertical asymptote
• Graph the horizontal asymptote, if it exists
• Graph the slant asymptote, if it exists
• Find at least two values on each side of the
  vertical asymptotes to put the picture together
• Use the calculator to check
• Note Factor the numerator and denominator when
  possible. If a factor cancels out, then it is
  not an asymptote, but the function still cannot
  equal that value.

4

• Y-intercept f(0) 2
• X-intercept x2 0, so x -2
• Vertical Asymptote 1-x 0, so x 1
• Horizontal Asymptote x x, so
• No S.A.
• Points

5

• Y-intercept f(0)
• X-intercept ,
• No real roots
• 3.Vertical Asymptote
• x-2 0, so x 2
• 4. Horizontal Asymptote
• x2 gt x, so none
• 5. S.A. long divide, ignore remainder
• 6. Points

6

• Y-intercept f(0)
• X-intercept x -1 0, so x 1
• Vertical Asymptote
• x-3 0, so x 3
• 4. Horizontal Asymptote
• x x, so
• 5. S.A. none
• 6. Points