Rational functions
usually have interesting asymptote behavior.
Asymptotes exhibited by rational functions come in different flavors, as shown below:
![]() horizontal asymptote The dashed red line is horizontal. The blue curve is getting closer and closer to this horizontal red line as $\,x\rightarrow\infty\,$ and as $\,x\rightarrow -\infty\,.$ Thus, the red line is a horizontal asymptote. |
![]() vertical asymptote The dashed red line is vertical. The blue curve is getting closer and closer to this vertical red line as $\,x\,$ approaches a finite number (from the right, and from the left). Thus, the red line is a vertical asymptote. |
![]() slant asymptote The dashed red line is not horizontal, and not vertical. It is ‘slanted’. The blue curve is getting closer and closer to this ‘slanted’ red line as $\,x\rightarrow\infty\,.$ Thus, the red line is a slant asymptote. |
![]() asymptotes that are not lines The dashed red curve is not a line. The blue curve is getting closer and closer to this red curve as $\,x\rightarrow\infty\,$ and as $\,x\rightarrow -\infty\,.$ Thus, the red curve is an asymptote that is not a line. |
On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. |
PROBLEM TYPES:
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