Precalculus and Advanced Topics Module 3, Topic B, Overview

Students Discussing School

In Topic B, students explore composition of functions in depth and notice that a composition of a polynomial function with the function f(x) = 1/x gives functions that can be written as ratios of polynomial functions.  A study of rational expressions shows that these expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.  Students apply these operations to simplify rational expressions and go on to graphing rational functions, identifying zeros and asymptotes, and analyzing end behavior.

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Common Core Learning Standards

CCLS State Standard
A.APR.7 (+) Understand that rational expressions form a system analogous to the rational numbers, closed...
F.IF.7.d (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are...
F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically...

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