Compare and Contrast Graphs of Rational Functions

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Students will be able to compare and contrast the graphs of rational functions in the form y=a/(x-b)+c and describe the differences and similarities of these graphs using academic vocabulary.

Big Idea

Engage students in the higher-order thinking task of comparing and contrasting rational function graphs using academic vocabulary while reviewing all essential skills of the unit.


30 minutes

There is an extended warm-up provided for today, which you can choose to use or not. The idea is that students can use the day to begin preparing for the summative assessment of this unit. The extended warm-up includes problems related to each key skill of this learning unit in the same sequence that they were covered during the unit. Direct students to choose the problems that they want to focus on because obviously 30 minutes is not enough time to tackle all of the problems.


Some students may have fully mastered all of these skills during the unit, so the challenge warm-up is provided for them. Creating graphs to match the approach statements turns out to be quite difficult. If they accomplish this with graph sketches, you can ask them to find equations that would match those approach statements as well. This is incredibly challenging for some graphs, and will require some piece-wise functions.

Investigation and New Learning

30 minutes


10 minutes

These questions require students to generate pairs of functions that fit the given requirements. It is like working backwards from the classwork. Some students might refer to problems on the classwork to find their examples. I would encourage them to try to generate their own examples first, and only refer to the classwork for confirmation or if they get stuck.


It is important to discuss these problems as a class to make sure that students end the class with correct examples. Have them share with each other, or put up two sets of examples for each problem and ask them to decide which pair of functions matches the given requirements.


The purpose of this discussion is two-fold: (1) to have students practice looking at the equations and identifying the key features of the graphs without actually graphing and (2) to use the key terms to describe the graphs of these functions more abstractly.