| | In this course, students gain more skills in equation solving,
analyzing graphs of functions, and modeling scenarios with
geometry and algebra using ASL for instruction. All of these
skills give students greater power to detect, describe, and
generalize from patterns they see in the world around them. By
completing rich problem sets, unpacking the arguments of
other students, and exploring complex examples with Desmos
(dynamic graphing software), students learn to make more
detailed conjectures about how the graphical features of
functions can be predicted from their equations. Through class
investigations, case-study problems, mini-projects and written
assessments, students will demonstrate their capacity to solve
problems, describe patterns, and justify their reasoning.
During this course, students explore exponential functions
across continuous domains, which leads to developing a
deeper understanding of fractional exponents. Logarithms are
introduced as the inverses of exponentiation, and students
explore the properties of logarithms to solve more complex
problems with unknown exponents. Students explore the end
behavior of polynomials and rational functions, the concept of
asymptotes and multiplicities of zeros. Students learn multiple
strategies for dividing polynomials and they extend their
knowledge of graphing parabolas to higher-degree
polynomials. Students analyze properties of a library of
common functions (linear, quadratic, cubic, hyperbolic,
exponential, absolute value, and nth root) and their linear
transformations. |