Stitz and Zeager, Precalculus (3rd ed.) – Available free online
The following table lists the minimum set of topics to be included in this course. The number of lectures listed for each chapter is only a suggestion and will vary across instructors and semesters.
There are typically 42-43 lecture days in a semester, so lecture periods are available for exams.
|1.1-1.7||Relations, Graphs, and Functions||6|
|2.1 – 2.5||Linear and Quadratic Functions||5|
|3.1 – 3.4||Polynomial Functions||6|
|4.1 – 4.3||Rational Functions||4|
|5.1 – 5.2||Function Composition and Inverse Functions||4|
|6.1 – 6.5||Exponential and Logarithmic Functions||6|
|8.1 – 8.5||Systems of Equations and Matrices||7|
OPTIONAL TOPICS (time permitting)
- Sections 9.1-9.3 on sequences, summation, induction, and counting
- Other outside topics, readings, videos, or materials the Instructor deems relevant
- Students can interpret and use mathematical notation and vocabulary related to the concepts of a function and the graph of a function.
- Students can compose functions, invert functions, and interpret relationships between inverse functions via composition.
- Students can identify shifts, stretches, and compressions of a function via its graph and its defining formula.
- Students can write and graph linear functions and solve linear equations.
- Students can use data to find and interpret a linear relationship between quantities in a given context.
- Students can write and graph quadratic functions in various forms, and find their vertices and roots.
- Students can recognize the shape of a power function’s graph based on its exponent, and model various phenomena with power functions.
- Students can write and graph polynomial functions, identify their end behavior, and use technology to find their local extrema.
- Students can find real zeros of polynomial functions by hand and using technology.
- Students can write and graph rational functions, and find their domains, zeros, and asymptotes.
- Students can write and graph functions representing both exponential growth and exponential decay.
- Students can define a logarithm, graph logarithmic functions, and use the properties of logarithms to simplify logarithmic expressions.
- Students can solve exponential equations and use data to find and interpret an exponential relationship between quantities in context.
- Students can identify inconsistent systems of linear equations, and solve independent and dependent systems of linear equations using Gaussian elimination.
- Students can multiply matrices, find matrix inverses, and use matrix inverses to solve systems of linear equations.