This course is designed to prepare students for college-level calculus and provide grounding for other mathematics and science courses. The course encourages students to develop a deep understanding of functions and their application in modeling dynamic phenomena. The framework delineates content and skills common to college precalculus courses that are foundational for careers in mathematics, physics, biology, health science, social science, and data science. Students study each function type through their graphical, numerical, verbal, and analytical representations and their applications in a variety of contexts. Furthermore, students apply their understanding of functions by constructing and validating appropriate function models for scenarios, sets of conditions, and data sets, thereby gaining a deeper understanding of the nature and behavior of each function type.
As a result of this course, students will be able to:
1. Analyze and describe key characteristics of polynomial, rational, exponential, logarithmic, trigonometric, polar, parametric, vector-valued, implicitly defined, and linear transformation functions in mathematical and applied contexts.
2. Solve equations and construct equivalent analytic representations.
3. Construct equivalent graphical, numerical, verbal, and analytical representations of a function.
4. Select, construct, and validate function models using transformations of functions and regressions based on the characteristics of a bivariate data set, characteristics of covarying quantities and their relative rates of change, or a set of characteristics such as zeros, asymptotes, and extrema.
5. Identify, interpret, and apply information from a function model for a given context or data set, subject to assumptions and limitations related to the context.