Precalculus/AP Precalculus

In this unit, students will explore polynomial and rational functions by describing and comparing how input and output values vary in contextual scenarios. Students will construct graphs that represent relationships between two quantities and use average rates of change, including changes in average rates of change, to describe important characteristics of functions. They will determine zeros, identify key features, analyze asymptotes, and describe the behavior of polynomial and rational functions using appropriate notation, including limit notation. Students will also rewrite and construct polynomial and rational expressions and identify or create function models that appropriately represent real-world situations.

In this unit, students will explore exponential and logarithmic functions, including how arithmetic and geometric sequences can be represented as linear and exponential functions. Students will rewrite, construct, and identify key characteristics of exponential expressions and apply exponential models to contextual scenarios. They will also examine function composition and inverse functions by rewriting, constructing, and evaluating functions and their inverses. In addition, students will rewrite, construct, evaluate, and identify key features of logarithmic functions, solve exponential and logarithmic equations and inequalities, and determine whether an exponential model is appropriate by analyzing the linearization of a semi-log plot.

In this unit, students will explore trigonometric and polar functions by constructing graphs and describing the characteristics of periodic functions. Students will use the unit circle to determine and construct representations of sine, cosine, and tangent for given angles. They will identify key features of sinusoidal and tangent functions, construct models that represent periodic behavior, and develop analytical and graphical representations of inverse trigonometric functions. Students will also solve equations and inequalities involving trigonometric functions, rewrite trigonometric expressions using identities, and describe, locate, and graph points and functions in polar form.