3-3 Oblique Asymptotes

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3-3 Oblique Asymptotes

• What? Oblique? I think that word was on my
  vocab last month.

2
OK to review for just a minute

• If a VA cancels out, graph the point as a hole.
• If a VA doesnt cancel out, plot 3 points to the
  left and right of the x value.
• FYI Both CAN exist on one graph. Just take
  your time.
• Do the warmup problem.
• Tonight, the problems will be like this one. I
  am getting you ready today for tomorrow nights
  homework!!

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So what is an oblique?

• Did you notice that all of the graphs that had
  vertical asymptotes also had limits? That is,
  the only functions that didnt have limits had
  holes.
• What if you have no limit to the function, but as
  well have a vertical asymptote?
• Such as, Lets go
  graphing!

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What happened?

• Well the vertical asymptote stayed, but the graph
  didnt level. There was a diagonal line that
  acted as a boundary line. This diagonal line is
  the Oblique Asymptote (OA).
• So, from this picture lets guess the OA and then
  lets see if we can figure out how to find the OA.
  

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Thats right!! (just watch this part)

• When the limit does not exist and there is a
  restriction, then there will be an oblique
  asymptote.
• To find the OA, long divide the denominator into
  the numerator and ignore the remainder. That
  quotient is the oblique asymptote. Then graph
  the function the same way as if there was a HA.

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Plot points and graph the function There will be
a hole
Check denominator of F(x)
Cancels
Doesnt
Exists
Plot 3 points on each side of VA
Take the Limit
DNE
Plot the OA as a dashed line then plot 3 points
on either side of the VA
Divide Denominator into Numerator
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So lets practice

• Graph the following completely.