• Precalculus Honors Syllabus

This course is designed for mathematically talented students who are interested in pursuing mathematics at an advanced level, particularly Advanced Placement Calculus. The course focuses on trigonometry, function analysis, and an introduction to calculus that is designed to prepare students for success in future advanced mathematics courses. Graphing, problem-solving, and analysis are stressed. Graphing calculator use is emphasized. The use of technology is infused with gathering, analyzing, and communicating mathematical information.

Unit 1:  Graphs and Introduction to Function Analysis

Review graphs of constant, linear, absolute value, quadratic, and radical functions as shifts, reflections, and/or stretches of their basic functions.

Numerically understand shifts, reflections, and/or stretches of graphs of functions and graph piecewise-defined functions.

Compute values of the domain and range graphically and analytically.

Interpret graphs of functions identifying intervals of increasing, decreasing, and constant function values as well as comparing the function to F(x) = 0.

Compare and contrast functions and their graphs.

Determine the domain and range of a function graphically and analytically.

Perform operations on functions, including the composition of functions numerically, graphically, and analytically.

Understand what it means for a function to be discontinuous and classify discontinuities as removable (point) or non-removable (jump or infinite).

Rewrite absolute value functions as piece-wise defined functions.

Classify functions as even, odd, or neither numerically, graphically and analytically.

Determine if a function is a one-to-one function or not. If a function is a one-to-one function, find the inverse of a function numerically, graphically, and analytically.