• 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 5:  Exponentials and Logarithmic Functions

    Use the properties of exponents to solve exponential equations by rewriting both sides of the equation as a power of the same base.

    Investigate graphs and equations of exponential functions. Classify exponential functions as growth or decay functions.

    Find equations of basic exponential functions, with and without technology, given function values.

    Graph exponential functions, identifying horizontal asymptotes and applying shifts and/or reflections to basic functions.

    Analyze exponential functions numerically, graphically, and analytically.

    Define a logarithm to be the inverse of an exponential and simplify simple logarithms using basic properties.

    Simplify complex logarithmic expressions by applying all the properties of logarithms. 

    Solve exponential and logarithmic equations using the inverse properties of logarithms and exponentials.

    Solve application problems involving exponential and logarithmic equations.

    Develop graphs of logarithmic functions, identifying vertical asymptotes, domain, range, and end behavior graphically, analytically and numerically