Day 51-52 - Rational Functions

Students worked on reviewing the ideas behind rational functions. The most important parts that we looked at included:

1. Finding the roots of rational functions.
• The biggest issues that students had with finding roots was checking that their answer was really a root. This relates strongly with the Habits of Mind, namely persistence.
2. Finding the vertical asymptote
• To find this, we first discussed how and why you cannot divide by zero. The students blogged about this.
• From there, we discussed the definition of what a rational function is and I asked what would happen if the denominator of a rational function were to equal zero at a certain input. This is where things got really confusing for the students.
• Graphing the rational functions helped explain what happens at these points. The ideas behind infinity and negative infinity seem to be difficult for some.
3. Finding the horizontal asymptote
• Because the definition of a horizontal asymptote involves a value that f(x) never reaches but gets infinitely closer to, I decided to teach horizontal asymptotes using limits. This may have been a bad idea since it ended up eating a whole week.
• I am happy that the scholars got to see an brief intro to limits at least.

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