3-3 Oblique Asymptotes What? Oblique? I think that word was on my vocab last month….

OK – to review for just a minute If a VA cancels out, graph the point as a hole. If a VA doesn’t 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 night’s homework!!

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 didn’t 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!graphing

What happened? Well the vertical asymptote stayed, but the graph didn’t 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.

That’s 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.

Cancels Take the Limit Check denominator of F(x) Plot points and graph the function There will be a hole Exists Plot 3 points on each side of VA Divide Denominator into Numerator DNE Doesn’t Plot the OA as a dashed line; then plot 3 points on either side” of the VA

So lets practice Graph the following completely.